Thats a bad mentality to take. Firstly, you're under the impression "a lot of damage" is always a good thing, which is pretty wrong. Second, Ryze raping other champions isn't necessarily a good thing either, because killing other champions doesn't win, knocking towers down does, and Ryze sucks at knocking down towers.

So, in answer, I suggest you find a champion you like. Get good with them, and start helping the team constructively, because if your aim is solely to "rape people" you'll fail badly at the game, and incur a lot of wrath from your teammates.

I'm thinking Ryze would probably be better especially for newer players, what with not needing to last hit mobs with your abilities to increase your ability power, and Ryze's short cooldowns and STILL being able to do a buttload of damage if you didn't build him correctly because his mana increases one of his main damaging ability.

I say go with Ryze, he hits like 5 trucks taped together crash landing on you.

I'd disagree. Ryze's spells aren't exactly long range, and if a Ryze tries to 1v1 me I'd gladly turn him into gold. He used to be a faceroller, just mashing buttons to win. Now he takes a lot more finesse and awareness after constant nerfs.

Try him by all means, but don't be surprised when you get trashed and converted into gold a little too often. Tristana is a good ranged dps to start with. Long range, 2 escape skills, good farming capabilities, and effective at all levels.

You might enjoy Veigar as well, he deals a lot more single-target damage allowing him to burst people down.

Veigar OWNS

I'd say annie would be your best bet, veigar can be good but you need a lot of setup and some luck to land some of his skills. With annie all you really need to be good is making sure your passive is active before you cast tibbers.

Annie

Annie is as easy, or easier to use as the other two, and overall a better champion if that interests you. Most people consider her to be the best caster for people to start off the game with.

Veigar is currently a little weak because not many champions run around with large mana pools anymore. Ryze is pretty strong early on but has a terrible late game. However if you have experience playing them and enjoy playing them, dont let that deter you from playing them.

as you can see, people hates ryze in the community, do you want to be hated by them?
Also you won't have many opportunities to play Ryze cause he's overplayed and almost in every match (not almost, 50% of the matches) you'll find a ryze.
I recommend you Veigar, but that's my personal opinion, I tend to play the most underplayed champions (the most uncommon) and most of times the worst ones only because I feel unique (I still need to find somebody who plays tryndamere) and because if I excel, I will feel lot more rewarded than if I go 19-0 with Jax or Ryze.
But well the conclusion is:
Ryze = easy win, commonness and boringness, you'll end fed up of the same combination of items/spells every match...
Veigar = skill, dedication, practice and a lot of frustration, but uniqueness. Oh haven't I told you veigar is considered an underpowered champ?