It's not particularly dangerous. Most safety comes with common sense (e.g. don't shoot towards anything that might have people). So long as you're doing that, you're more or less on the safe side.

Your budget is very limited. My bottom line for recommending a bow is at least $250 for a wooden takedown recurve with a set of arrows, which will give you a solid bow that is usable over a long period of time and is satisfying to shoot.

Bows in the <$100 range are cheap youth bows, usually made from fiberglass and have that cheap "plastic" feel. They don't shoot very well and arrows flop out of them. However, they're designed for the "dabble" purpose, so if that's what you want, you might want to look at something like the Barnett Sportflight.

I felt a little dirty recommending that.

I'd otherwise seriously recommend going to a club to try out archery, if that is an option.

Barnett Sportflight series is popular

http://www.amazon.com/Barnett-Sportflight-Recurve-Archery-Set/dp/B000R9QTFY