Go to the best & most hardcore archery store you can find. Get yourself "fitted", by a professional.
Don't buy the new $700 bow.
Instead, go on ebay and get a used bow that's the equivalent size, weight, and draw length.
I got a Hoyt Fast Flite bow a few years ago. I paid $90 on eBay. It was the flagship in 1995ish.
Some red-butt Alabama boy killed 40 deers with it, and finally upgraded.
I tweaked it, tinkered, changed the rest, etc.
It's not quite as light or nifty as the newest high dollar bows, BUT it's still wickedly accurate (even in my novice hands).
Bows are amazing, because they are VERY repeatable. IF you hold the same target, the arrows will hit the same spot. Vastly more accurate than a handgun (for me).
Below is a couple tries I took at severing a string on a straw bale. I was probably 20-30 yards away.
Almost pinpoint.
The difficulty is estimating range. Because the arrows travel so slow (in comparison to a bullet) they drop fast. IF you misjudge the range by a few meters, you're off the target.
(Note, when my form is sloppy or I get tired, I shoot to the left. But that 's a different topic.)
http://youtu.be/vF8Rmv-Iurc
Here's a video my boy shot. He caught me dusting the bow off.
BTW, the range and ammo is free for the bow. I've only had to retire 2 arrows in 6 years.
If I were to practive regularly, I could be very accurate. As it is, I only take the bow out when I "find" it in the closet.