best acurate hunting rifle

I'm going to break from the crowd here a bit. Instead of pointing you towards a more expensive or more powerful gun, I would point you towards smaller game.

If you truly have a need to hunt deer for food, I would suggest a typical centerfire rifle.

If you could accept hunting up to raccoon size game a used Marauder in .22 or .25 would be a great starting point. As pointed out you will need a hand pump at a minimum, but that will almost certainly take the enjoyment out of the experience. You would most likely need an SCBA tank and a place to fill it to 4500psi.

If you can accept hunting up to rabbit size game then you can get most spring guns in your budget new or used. If this becomes a hobby you enjoy you will never regret having a great spring gun. Many members here who have the best of the best PCP's will often post about the joys of just grabbing a tin of pellets and heading out for a day of fun with their beloved springer. The first adult airgun I purchased was a quality spring gun (HW77) and if push came to shove it would be the last gun I would part with. Something special about your first good airgun.

I see this is your first post.

WELCOME to the forum! Best bunch of folks in the industry live right here.
 
First of all welcome to AGN. I read your profile and see you live in Pa. as do I. In Pa. there is no big game hunting with air guns of any type or caliber and .25 caliber is illegal for small game hunting. The only calibers allowed for hunting in Pa. are .177 and .22 for small game only but .22 must be use for groundhog. So to answer your question if you are inquiring about a Pennsylvania hunt I would suggest you look at a Savage or Ruger in .308.
 
Fellow Airgunner,

If you want to be able to drop a deer ethically with a .25, I would save an extra $100 and get either 

the Airforce Escape, or the .25 cal Seneca Sumatra 2500. Both rifles easily fit pellets and slugs of various

lengths. The Escape I believe, is the most powerful production air rifle in the world, and the Sumatra is

the most powerful production small bore repeater in the world; under $1000. Best of luck.