How do I remove stripped screws?

What rotary tool would you recommend? I'm not knowledgeable about hardware (in regards to computers and crafts alike) so I don't know where to start and don't want to end up ordering a tool that will be too big or too destructive for such a small job.

The name Dremel is so well known that it's almost generic, like the way Hoover is (or used to be anyway) synonymous with vacuum cleaner.  Plenty of online research to be done, but the name Proxxon seems to be recurrent. I don't think you need to pay those kind of prices though, I have two very cheap Dremel clones that have always worked fine for me. Your local tool and/or hobby store might be a good place to see what's available and get more advice. Variable speed is useful.