So after a string of horrible matches I've dropped from high 1400s to the dreaded low 1000s. Originally I played a tank/support character to get out this ELO bracket, but no matter how well I support / tank - if the carries aren't there; we lose.

Now I don't have loads of experience playing carries, but I am wondering what is an easy one to pick-up and play, but who is also very effective, especially in lower ELO games and usually capable of carrying the team to a win.

Tristana, Miss Fortune, Ashe ...if well farmed.

I like Tristana for an easy carry. Ryze can be decent too if you are playing the dregs. (Ryze is the only character with whom the bot player is indistinguishable from the real player)

When you go from Tank/Support to a damage dealing carry it is never really a matter of "which is easiest to play" it's more of a mindset change. Knowing that you can't just rush in every time like a gungho tank - know when to fight - know when to run.

That being said - when you first start to play a carry I would build safe builds first - to let you have room to make small mistakes just to help you learn skill sets and enemy setups better.

Safe meaning - say you picked Ryze for example - get a Rod of Ages. Health - Mana - AP. Mainly for the health.

Or if you picked Tristana - get something that will help you lane more - Vamp scepter first for lifesteal - Frozen mallet for the health and utility.

I'm going to go out on a limb and recommend Mordekaiser. I know, not a true carry, per say. However, he's one of the few champions that can, if overleveled and well farmed, carry his team, kicking and screaming, right to the Nexus.

Why?
He can easily dominate a solo lane against an unskilled or easily intimidated opponent... and it's very easy to intimidate with Mordekaiser.
He can easily out-farm and out-level an opposing lane because he can jungle and lane at the same time.
He can quickly push and apply pressure to towers, and killing towers wins games, not kills.

Just my opinion, take it with a grain of salt. My main reason for suggesting him is durability. Tristana and Ashe are 'carries', per say - but even if fed, can be focused and crushed, leaving your team with no effective damage.

Tristana is easy to play but the game can fall apart before you can carry. She needs many minutes of pure lane farming to begin to carry.

Someone who can take control earlier in the game is Mordekaiser. He will start romping and stomping from Level 1, and while he loses a little bit of steam at 18 to pure carries, you can have game momentum heavily tipped in your favor by then.

I have played Ashe, Olaf, and Tristana in the past and I agree: they seem to either take forever to farm up, or I can't seem to do enough damage.

For example, with Ashe, while I can slow and shoot arrows, they don't seem to do enough damage before more enemies show up or they ghost/flash/voidwalk/etc away.

Olaf: I can quickly clear the jungle, hit the dragon by 4, but when I go to gank, even with help and a red buff, I don't do enough damage before they can slip away.

Tristana: Unless I am mid, I have trouble farming up and an underfarmed Tris, to me, seems fairly useless.

I think I might give Morde a go.

Any other suggestions?

Last hitting is top priority.

Miss Fortune is the easiest carry to pick up and play for anyone.

Tristana is easy if you're experienced at LoL and have good fundamentals like positioning and last hitting.

Ashe is fairly easy as well.

I suggest Ashe. Like all carries, her damage isn't amazing until you've farmed, but her ult brings stun to the fight. That stun can help you keep allies alive, ensure a kill on a target, keep yourself alive, whatever. Trist can only knock an enemy back and MF can only slow an enemy down (which you can also do, conveniently). She doesn't have Rocket Jump for a panic-button escape but I believe Ashe brings more to a team fight than Trist can.

As for Morde, he is iffy. If you have a bad start in the slighest, you will do very little for your team the entire game. You have to have an amazing start and keep pushing the advantage, because as late game comes around your damage is going to drop drastically while enemies can take down your shield faster and the fact that you have no CC becomes more apparent. Your best hope late game is to Ult their carry and hope that can win it for you. In other words, Morde CAN be good, but he is not a carry.