There is a hge difference between using a sight on a recurve bow and shooting instictively. With a sight the bow MUST be held vertically and your sight are set for various yardages. Shooting instinctively the shooter usually has the bow canted (top to the right for a right handed shooter). This is an advantage actually for hunting because you can shoot at various positions like standing, kneeling, even sitting. Shooting instinctively is like throwing a rock or baseball. You don't aim. You just haul back and throw. With practice you get better and better with your accuracy - same with the recurve. And maximum effective range is also personal. Again, look at a baseball player in the outfield. If he was limited to 25 yards he could never throw a perfect ball to the catcher covering home plate. That is why practice with a recurve (or longbow) is so important. And practice does not make perfect. PERFECT practice makes perfect.
My advice if you have it is to go to an archery pro shop that deals with traditional equipment and let them show you the proper form. A good read is "become the arrow" by Byron Ferguson.
What I can tell you is that your grip, anchor point and draw length must stay consistent for repetitive accuracy. Shoot at a 2" circle at 10' first. Only shoot maybe 6 - 10 arrows and do this for several days. Yes it sounds boring but it works. Then go back to 20 feet then 40, etc. With proper and regular practice your effective range will increase. If you can get it out to 30 yards you are good for almost all bow hunting in the woods as most shots are even less than that. Not sure what your terrain is in OK but if its more open country you may have to extend your effective range. That's a lot of practice but possible. Good luck