You are talking two different languages. First, you wanted a rapid firing 22 auto, now you want accuracy. Make up your mind.
If accuracy is important, which it would be to me, get a bolt action rifle with a detachable magazine. If you have time, look at guns shows, as well as the old time shops that sell a lot of used equipment, and look for something like a model 69 (or 69A) Winchester, some older, accurate Remington, a good Mossberg, or a whole host of other, more accurate, and maybe pricier, rifles out there.
Same applies to a hunting rifle. Why are you hung up on an auto loader? There is no reason an auto loader is needed for hunting. Get a rifle with an action of your choice, that you have to operate to bring the next cartridge to battery, learn to shoot it well, and you are fully, and adequately, equipped.