This would probably be better in the hunting forum. You'd get more responses. Personally I like shooting traditional. I have a 70#recurve. I'm headed out for elk with it this friday. You could probably pick up a good hunting or target longbow or recurve for less than $300. Check Cabelas website. I had mine custom made so it's a bit more pricey. My first hunting recurve cost me $175, used.
Entry level compounds cost about the same. Compounds are much easier to get into but can cost a fair ammount with all the available accesories. Compounds are eaiser to draw as they have a 60% letoff when they are at full draw. They generally have sights, are very compact, and shoot remarkably fast. Add to that a mechanical release and you have a bow that is hard to miss with at known distances.
That being said. I like the feel and romance of shooting with traditional equipment. Instinctive shooting feels right to me. Just getting to the point where you can make a consistant accurate shot takes a fair ammount of work and is something to be proud of. Just yesterday when I was practicing in my yard a neighbor shouted from accross the street as he walked by, "Wow, not many poeple use a recurve any more." I could hear the surprise in his voice, he was obviously impressed. Good thing he didn't see me put an arrow into my fence.
It really is a matter of personal taste. I'd say go to the local range and see if they have a couple bows for you to try out. Then get a longbow or recurve (ok, so I'm biased)
This is the guy who built my bow, he makes Recurves and Long Bows:
Wes Wallace BowsSome other useful places to visit:
StickBow Three River's Archery