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Tristana is a good beginning hero to try out imo, and I've been playing some games with her lately, even though I just started this game a few weeks ago. Good carry, insane damage; just be sure to focus on last hitting the first 6 levels of the game though.
I'm a weird person with weird taste, and I might get flamed quickly. Vladimir is also a good preference of mine when I first started during the last few rotations they had if you are just starting out. I wouldn't recommend it since it's 6300 IP and you might not like him, unless you want to consider being a vampire-like caster who blows stuff up and can be really good if played right.