Just wanted to introduce myself before I write this post (may be long sorry), I started playing LoL about 3 weeks ago. My floor mates at college got me addicted and now we play together most nights. I started off playing support with Allistar, Janna, and Nunu. (felt boring after a while) Eventually I started to play mid with Kat and Morg. I really enjoy mid, but I cannot seem to hold the lane late game. I always end up getting ganked by the enemy team. I also get less farm than the enemy mid. I think that practice may get me better, but if you guys have any tips to help me play middle lane that would be awesome. And one other thing, I have over 5500 IP saved up to buy a new champion, but I am not sure who to buy. The only AP carry I own is Kat, and I feel she is too offensive for me. I always seem to get out ranged when I play her or I try to farm and I get stunned, then wreaked by the enemy. If you guys have a good AP mid for me to try than please let me know, or tell me if I should just stick with Kat and try and get better with her. And if you read this far, thanks for reading and I would really appreciate any advice you can give me.
Edit: Forgot to mention my name *facepalm*, anyways it's Ryan

Late game is usually after the 25-35 minute mark. This is the point at which builds are coming together, team fights are starting, and laning ends. At this point, if you are still pushing and doing so while alone, there is a higher chance of being ganked by a larger group. HOLDING a lane, and by that I mean defending at the tower is fine, however pushing out to the middle or passed river is asking for trouble.

By late game you need to be team fighting to win.

Annie is free at the moment and is also refunded the entire mana cost of her Q when she last hits with it. Other mids have longer range and burst, but she is very well balanced for new players. Anivia is also free-to-play and has the ability to farm VERY quickly. Always make sure to play the free week champions until you find one you really like.

Yea I think that I have trouble deciding when to leave my lane, and I think I will try out Annie. Thanks for the help, but what other champions do you think that I should look at since I have a fair amount of IP.

Every single mid if you really love the role >,>

I still think free week is the answer you need though. You could easily end up with a champion you never play.

In the mean time I don't have just one favorite as they all have their own strengths. It would honestly be easier for me to name the mids I don't own @___@

Since you have trouble deciding when to leave lane, you should try out champions who shouldn't stay mid. I feel that will acclimate you better since you will be more aware of the state of the game, simply because that's how those champions play.

You should try out Evelynn, Kassadin, Twisted Fate, or Ahri. All of them are good at ganking, plus Kassadin/Ahri are hard as hell to gank while Evelynn/TF are hard to keep track of.

Mid was the first role that I learned and I still love it immensely even though I mainly play AD Carry nowadays. Farming is extremely important in both of those roles.

If you're having trouble with keeping up with your opponent in farm or you're just getting harassed too much and not used to dealing with it yet, try picking an AP mid either with a good escape or someone who has good range. Morgana is good in this case because she is very efficient and farms very well with her W from afar.

I personally also love playing Lux mid as she was the first mid I ever learned. She out-ranges most of the other mid champions so you can harass and farm from a good distance without having to worry too much about ganks from the Jungler.

Annie is a good choice since she is free, but she is extremely susceptible to ganks and really has no escape outside of a stun and run. If you get caught its pretty much a free kill. You can always try out Anivia as well since she is free this week. She can put down a wall to block opponents from getting away, break up groups in team fights, or protect yourself from a pursuing enemy. She's also really fun and does good damage, although a bit more challenging to play than someone like Annie.

I second V1rtuE's recommendation of Lux. Her range is phenomenal, she's pretty beginner-friendly, and she can do some very nice bursty damage at a huge distance in late game, compared to Kat who is a lot more close-range. Lux is also very similar to Morgana, who you already have some experience with. She's just a bit more distance-oriented than Morg.

Xerath can also pull off some ridiculous range, though I find him a fair bit more difficult than Lux.

Ahri is also another potential good choice. She's somewhat similar to Kat, so she may work for you.

And while not AP, Caitlyn might work for you as a mid laner. She's got the longest autoattack range in the game, so you can hassle a lot of common mid laners without putting the same strain on your mana that they'll have to put on theirs to keep pace with you.

And as others have said, late game is definitely not about pushing lanes on your own. Try to stick relatively close to at least a couple of your teammates to avoid being ganked as easily, and be wary of wandering too far from your turrets alone, especially when you can't see a lot of the enemy team anywhere on the minimap.

Hey man, don't give up on mid! It's the place to be. Let me see if I can give you a few pointers

FARMING

Since AP champions tend to have lower AD stats (especially since you wont be running those runes or masteries) its reasonably harder to last hit creeps with autoattacks in the middle. Its going to take some practice for you to be able to do this more efficiently. Try to get the feel for the champion you are going to play with their autoattack animation and missile speed (the ranged animation like Morgana's little purple bolt thingy) because they are all unique. However, the increased ability power gives you an alternate method of securing minion kills with your abilities! Most typical AP champions have their own unique process of using their abilities to secure minion gold. For instance: Morgana's W can kill full health caster minions at ability rank 3 with 20 AP. Since caster minion's come into lane with melee minions in front of them, you can place a pool under them as soon as they stop for 3 guaranteed minion kills. Experiment with other champions and find out what works best for all of them, or watch videos/ask people and emulate their strategies, you'll be a farming boss in no-time.

GETTING GANKED

Don't feel bad. Everyone gets ganked. The good news is every single gank is %100 preventable. Obviously you can't just sit under your tower all day, but there are some skills you can work on to help you out with your unfortunate deaths.
MAP AWARENESS: As you'll play more league of legends, you'll develop an uncanny ability to point your eyes different directions, focusing both on your champion and the minimap. I'm kidding of course, but you do need to watch the minimap. If you can see all 5 enemies on the map then you know exactly where every single one is right? But if you can only see 4, then you know one of them can be in any single dark position on the map. See 3? 2 could be anywhere. See only 2? 3 could be anywhere. Its actually a scary prospect, but use logic to your advantage. If you can only see 4, but you know bottom lane got a kill 10 seconds ago, you shouldn't have to worry about the 5th enemy who just spawned instantly ganking your lane. Inversely, if you are close to your opponents tower and you can only see one champion in every lane (3 enemies) its probably pretty safe to assume at least one of them is coming for you. Also, when you are chasing for a big kill or really focused on something happening to your champion, that's likely when you will need (and forget) to check the map most and make sure enemies aren't coming after you for starting a fight, or running from an ambush. There are infinite situations to cover, but think about it logic, and think about what you would do if you were playing your own team in the situation you are in (my teammate is nearby so I can be more aggressive, so if they are being overly aggressive they might have teammates nearby), and respond logically. You'll do better.
WARDS
Everytime i play mid, when I go back and finish buying items, I spend whatever is left on at least two wards. I then ward both bushes. It's worth the 150g to feel safe. Its worth the 150g to be able to let your team know where the enemies are going. Its worth the 150g for you or your team to perhaps pickup a kill because the enemy thinks they are hidden. Its worth the 150 to prevent what otherwise would have been a gruesome demise. Just get into the practice of doing this. You think it would be easy to remember, but getting caught up in a game makes it easy to forget. More vision gives EVERYONE on your team more certainty over map awareness, and enough cooperation from everyone warding in the right spots guarantees you victory. Think about what makes teams comeback from being behind, the element of surprise right? Whats better to secure a victory or make a comeback than the element of surprise, and whats better way to keep or foil the element of surprise by revealing someone's position? BUYEM. PLACEM. WIN
CROWD CONTROL
If nobody has explained this to you yet, crowd control is an element of any ability a champion has to disrupt how another champion works. Some examples are slows, stuns, knockbacks, silences, fears, taunts, suppression, etc. It's really important to understand the capabilities all the champions your are playing with and against have in terms of crowd control to maximize the potential of your team, because if your champion has crowd control you aren't using, you are hurting yourself and your team. A simple example of using crown control to your advantage is getting ganked as morgana. Lets say the enemy alistar enters your lane from behind because you weren't watching the map, and you know alistar can knock you closer to the enemy katarina and the enemy tower. However, you remember that morgana's E (black shield) can block abilities, so when alistar tries to knock you closer to katarina, your spell shield blocks it and you escape rendering his CC useless. Angry that you got away, and confident in a 2v1 situation, Alistar and Katarina chase you all the way to your tower, and you know you don't have enough damage for both of them, so as soon as you see one of them come within range of your tower, you use morgana's Q (dark binding) to BIND them so the tower can attack them multiple times and they cannot escape. Finally, seeing that you are getting dived(chased to your tower) your friendly master yi came down from toplane and enters to help you out. Since you don't want the enemy alistar and katarina to escape, you use Morgana's R (soul shackles) to slow them, and then stun them, allowing master yi and you to finish them off without them escaping. Using all of Morgana's ability to deny and use crowd control turned a 1v2 situation into a double kill for your team, Katarina could not have done all of that. However, should you have not used your crowd control, and negated alistar's, Katarina would have been able to kill you easily, picking up the cooldown reset on your death to use all her abilities on the master Yi that just wanted to help. That was just one situation that could go good or bad depending on circumstance. Knowledge is power, so give yourself the edge to understand champions and their abilities

Hopefully that helps. Good luck to you sir, feel free to ask me questions or add me ingame.

As far as farming goes a post 6 Anivia (she's free this week, give her a try) with either blue or a chalice of harmony is the easiest farming you'll ever get. Push R and clear the wave. Pushed past the middle of your lane? Ask you jungler if he minds you taking Wraiths or Wolves (push R again... though you'll take a bit of damage) or if you are confident that you wont get punished for it go steal the opposing wraiths.

While this is pretty much farming easy mode you should really get a feel for what your chosen mid laner wants to do to farm. Some like Annie or Ryze are single target farmers who use their Q or auto attacks and have a real problem pushing the wave out while others like Morgana and Anivia push a button and practically clear the entire wave. Most mids however will not be encouraged to burn their abilities solely for farm as it cuts into their burst potential as well as putting what may be a killing / saving ability on cooldown. People like Ahri, Cass and Orianna get abilities that can both farm and poke at the same time so you may want to look into them when they are on free week.

As for Kat and farming the theory is, in a vacuum you'll toss a bouncing blade and then clean up with a sinister steel. In practice this might be a bit harder with an enemy harassing you though if you want to go aggressive you chuck the blade (at the opponent) and are preferably in sinister steel range so you can keep shunpo in your back pocket as an escape (or an all in popping Death Lotus immeadiatly after jump). If they arent in range of steel you'll likely stop there unless you can get a kill with sunpo -> sinister steel ->Death Lotus. Be wary of ganks with this as you'll push the heck out of the lane and be on top of the opponent as well (go take wraiths or something to reset the lane).