If you want cheap you have to look used. Most are old bows sitting around and might need a string. They don't go bad unless they are abused. I bought a Bear Black bear for $15 at a yard sale.
Long bow and recurve is just what you like the best. Both work and in the traditional world longbows are just like recurves without the tips bent. Traditional long bows are laminated just like recurves. A long bow to be is a yew selfbow.
I bought some of this guys bows for my kids. The Pilgrim Line and they worked really good and is a really good deal.http://www.elkridgearchery.com/
Make sure you don't overbow yourself. If you shoot a 70# compound you might only be able to hold a 55# recurve without shaking at full draw.