New install - do character transfer?
Of course, the only data you have lost is game settings and screenshots (if you took any).
Your account information is stored in the data centers in Texas or Germany, depending if you are NA or EU. The download is for the client itself to access your account.
Technically no, nothing transfers over when you re-install the game.
But that’s because none of your account information was on your computer to begin with. It’s all saved on Anet’s servers.
So all you need to do is install the client, log in as normal and you’ll have all your characters, items etc. just as you left them.
(For future reference/anyone else whose wondering, this also means you can play your account on multiple computers without doing anything special. Just log in, from anywhere, and you’ll have access to your account.)
“Life’s a journey, not a destination.”
Obligatory cautionary addendum to Danikat’s final point: If you play from a publicly accessible computer, eg a campus library or an internet cafe, your account is greatly at risk of being hacked. Take all necessary precautions to make sure no one else can figure out your password by watching you type it or more subtle chicanery, or access your game while you take a bathroom break.