Stick with traditional archery. It's simple, like throwing a baseball. All hand eye coordination, no fiddling with sights, straps, couterweights, wheels, arrow rests, etc. Just put an arrow on your string and shoot.
As someone already mentioned, check out tradgang.com They also have a classifieds section you may want to keep your eye on.
I'd look for a cheap recurve, you should be able to completely outfit yourself for less than $200. I think I got my wife her bow + 6 carbon arrows + glove for ~$150.
Number one Tip -
Don't over estimate your strength! Archery uses muscles you don't use anywhere else, even at the gym. Stick to about 25 - 45lb. draw weight, or whatever is comfortable to shoot 30 arrows in a row.
If you want to hunt, 40lb. is the minimum in your state(CT). Some states are as low as 35lb. and in CA there is no minimum. If you stick with it, you'll get stronger and you can upgrade later, but there's no reason to get bad form because you're using too strong of a bow.
Look for a local archery club/range in your area. Talk to them. Look for a local archery shop and go test shoot some bows. Most shops also offer lessons. My wife got 6 free lessons with her purchase.
Here's a good example of something that will get you into the sport without dropping a lot of cash, and that will serve you well until you decide you love archery so much you want to spend $800! Another great thing about trad, is that you don't have to spend thousands to be good. A good trad archer will win a tournament whether he's shooting a $100 or a $900 bow.
20-35lb. -
http://www.pse-archery.com/products/category/445.5.1.1.16352.74370.0.0.0
35-50lb. -
http://www.pse-archery.com/products/category/Stalker/445.5.1.1.16352.7365.0.0.0
Cheap Target: Stuff a burlap sack, or 40lb. dogfood bag full of plastic grocery bags, and stitch the top closed with cord, wire, etc.