I've been looking at a few champions and playing lately with the current free champions. The one I'm liking the most so far is Miss Fortune, but Ashe was pretty good in the tutorial as well. I don't like REALLY squishy people, so I'd prefer someone that can at least take more than a few hits (unlike Veimar and some of the mages), but I do prefer someone with good range and damage. Champions I'm mainly considering are (in no particular order):

-Miss Fortune

-Ashe

-Caitlyn

-Corki

-Ezreal

-Graves

-Janna

-Karma

-Kog'maw

-Tristana

-Twisted Fate

-Twitch

-Vayne

-Lulu

I know it's quite a list, but any help or reasons you would consider one over the other? Like I said, I'm looking for range, damage, and someone who isn't extremely squishy. (I understand someone who's ranged isn't also going to be a tank, but someone who can stand a chance for a moment is preferred.) I'm getting decent vs bots, but am just getting into PVP and I want to make sure I find a solid champion to work with. If you want to know any other questions that may help in my selections or have any tips on how to use them and with what setups, I would appreciate it!

I've heard graves is a little more durable due to his passive. And his roll/ult is good for running.

The thing about Graves, he has the second lowest range of all the ad carries. Lowest is Sivir with 500, Graves at 525.

If you're going to run a ranged team, it means its a poke comp. A good choice would be champions like AP TF, AP Nid, Caitlyn (650 range), AP or Ad Kogmaw (500 basic range, 710 with W and his R has crazy range too)

Most of the champions you picked out are ranged AD champs (who are usually pretty squishy), with some supports too. You won't find many ranged champs that are also beefy (that wouldn't be too balanced!). But if we're looking for some that have built-in survivability, there are a few options:

Graves: His passive gives him stacking Armor and Magic Resist as he fights, which is pretty nice. His range isn't super-high compared to some others though, so keep that in mind.

Caitlyn: She's good at staying away from danger, thanks to her long auto-attack range, her traps, her net, and her long-range ult.

Tristana: Similar deal to Caitlyn. Her passive gives her more range as time goes on. She also has a jump to get away, and her ult can push people away from her.

From your list, I think those would be my suggestions. Graves probably moreso than the other two.

If we go off your list, there are some other champions that have range and survivability. These aren't all AD carries, nor are they even all AD champions, but I think they all bring some combination of range and toughness:

Urgot: He's a weird AD carry / Fighter hybrid. He IS ranged, and his harass range is HUGE. But he also has a shield and his ult often puts him in danger, so you need to build him more tanky than other AD carries. Nevertheless, he might fit what you're looking for pretty well.

Nidalee: She can be built AP or AD, but is getting popular as an AD champ. She has ranged attacks in human form (but melee in cougar), is hard to catch while in cougar form, and she works if you build her a bit bulky.

Gangplank: He isn't ranged, but he does have a low-cooldown ranged attack spell. And it can crit for major damage. He can also remove CC effects from himself, has a global ult, and his passive helps him stick to his targets. Make sure you build some health and resists though; so-called "glass cannon" Gangplank WILL get melted quickly.

Ryze: Ryze is a mage, but he scales off of mana, not AP. This means you can (and should!) build Frozen Heart and Banshee's Veil on him, which make him pretty tanky. He is a sustained damage mage, so he plays more like the AD carries than say, Brand.

Vladimir: He is also a mage. His passive gives him AP for building health, and vice versa, so he can get fairly beefy too, thanks to items like Rylai's Crystal Scepter. Also a bit more of a sustained damage mage, with decent AoE damage.

Hope that helps!

[EDIT]: Reworded a few things to make my points/suggestions more clear. Thx Panzer for pointing out the possible confusion about roles.

'Some of the beefier AD carries are...' *list of some AD carries and some non-AD carries*

>.<

As you said, Cait and Trist can be hard to catch (so can Kog in that respect, more so even), but that doesn't make them 'beefy.'

Urgot is a really weird AD carry, because he really isn't an AD carry... he's an Urgot, nobody is quite like him.

Nidalee is almost always built as an AD bruiser, sometimes support, and on the rare occasion something else.

GP is a beef (though he varies on the scale from super beefy to fairly fragile melee depending on the build).

Ryze and Vladimir... as you said, mages. (Not AD carries.)

Quick noob question. AP? AD?

For what....

Erm...what? Roll and ult is good for running? That's Vayne. Graves has a dash and a giant explosive shot for his ult.

No, noob question as in what does AP and AD mean?

Attack damage vs ability power. The term refers to the type of item you build to scale your damage.

AD carry-generally does more auto attack damage but has weaker abilities. Tends to go bottom lane with a support in the current meta. Almost always ranged character, but Master Yi and a few others could also be considered an AD carry type.

AP carry-does most damage with your abilities. Tends to go mid to level up faster so you can have higher level abilities so you can blow stuff up faster.

AD carries are generally going to be squishy. Many have one ability to help them get away, but will tend to go pop. Urgot is really the only AD carry that isn't so squishy, but he's also more of an "AD caster" in that he does most of his damage with his abilities and lacks a "steroid" ability to beef up his auto attack damage. He's a fun hero to play but is definitely not your typical ranged AD carry.

AP carries generally end up being tankier. They are (generally) more powerful early to mid game. They (generally) bring more CC/utility to the fight late game. Compared to AD carries, there are more options to get tanky with the caster items (Rod of ages, Rylas, Hourglass, etc). You may want to look into the AP carries more. Annie is pretty easy to learn, Brand is really strong, Morgana's easy to farm with and generally good. Lots of options. You're just going to be relying on your abilities more for damage than auto attacks.