Hi, Jason. You want to hunt or just shoot? It makes a difference. Before you think about which bow, decide how much money you want to spend. A compound hunting bow can easily cost a month's rent plus the better part of $100 for a dozen arrows and some must have accessories. Starting with an arm guard. Relax, it doesn't have to, but it can. A used compound bow isn't a bad thing.
If you just want to shoot go with a recurve. Arrows can still be the 'C' note, but don't have to. $50 to $60 will get you a dozen wooden arrows. The arm guard and shooting glove are required. Depending on where you are, a Cabelas store is a good place to go.
Go to a bow shop, get measured for arrow length and talk to them. Buy a copy of The Archer's Bible and start doing upper body exercises. Never buy any bow that has a draw weight of more than you can easily lift said weight. You'll hurt yourself. You use muscles pulling a bow that you use for nothing else. Back and shoulder. When you get a bow, any bow, push the bow away from you as you pull the string. You should be at full draw when you've raised the bow to eye level.
Venabulum, bow shop. Your needs are not the same as your kid's. There are both compound and recurve sets made for kids that don't cost a ton of money. I'm in Canada, for about $60Cdn you can get a set in either with a few arrows and the vital arm guard. Trust me, an arm guard is essential. But go to a bow shop. They'll have what you need for both of you. And training.