I'm not sure whether I'd want a compound, recurve, or long bow because I don't know enough about the pros and cons of each.
Why do you want to bowhunt?
It all started when some guys who liked archery wanted to hunt with their bows as well as shoot at targets. Those guys like learning and practicing the skills of their ancestors. It's a game for grown men and women -- you can play Robin Hood or Maid Marion, play Indian, or play Mongol warrior. Different kinds of bow go with different fantasies. There are also differences in performance between different kinds of bow. In order from worst to best performance:
English long bow
American flat bow (based on American Indian designs, but the Plains Indians also used recurves)
recurve
compound
It was difficult to get close enough to a deer with a bow during gun season when the deer are spooked by the swarms of hunters trampling the woods, so they lobbied for a special archery hunting season. That was when another group got interested in bowhunting -- guys who like
hunting, can't get enough of it, who bowhunt whether they have any interest in archery or not just to get a chance to do more hunting. That group isn't into the fantasy so most of them use compound bows -- developed in the 1950s, not fitting any historical fantasy, but more efficient than any of the traditional designs. Some of them prefer recurves for simplicity and reliability ... recurves are cheap since the development of wood and fiberglass laminates, too. They tend to load their bows down with gadgetry to help them get their deer -- sights, arrow rests, stabilizing rods, etc.
Some go to the opposite extreme and make their own primitive bows and arrows and even chip flint arrowheads. Some of the guys who start out with high-tech monstrosities end up going primitive. One reason is to make hunting more of a challenge. After you've achieved your first goal of getting a deer with a bow, maybe achieved it many times, you might get bored with that and want to make it more difficult.
The first step is to decide whether you just want to get a deer any way you can or you want to play, and if you want to play what role do you want to play?