BigJim's right; I'd go with a recurve. Something in the 40-50lb range would be great. Alot of people shoot lighter poundage and do just fine. I shoot a 55lb recurve most of the time, but I like taking longer shots than most.

And, as BigJim said, you can find a compound for alot less than $75-$100 at garage sales or even archery pro shops. I have a nice little Jennings that's perfect for bowfishing, and I paid $35 for it at a garage-sale. Look for something that has wheels instead of cams. They're easier to draw fast. And look for something a little longer axel-to-axel, so the string doesn't pinch your fingers.