Here's your requirements, as I understand them:
I'm looking for something 1) I can reload 2) for the range only right now 3) extreemly accurate 4) doesn't require a second mortage. What are the suggestions?
1. You can reload for just about darned near anything. Sticking with common calibers will increase your choices in components if you want to experiment a lot. A good press and dies are worth buying, as you should expect at some time to be FL resizing, although you can get by in the little Lee Loader - which takes you back to common calibers.
2. You use the prhase, "right now." If hunting is secondary, "right now," then you can look to a milsurp arm. They are usually heavy and have less-than-desirable trigger actions, so for hunting they take a back seat. You CAN hunt with them, but most folks use them for just shooting and having fun with. But, I get the sense you are talking about an Omni-Gun, a multi-tasking, commercial grade weapon. Read on...
3 & 4. Uh-oh. Any time you put the word "extreme" in a description, you jack the price. Think about it, "extremely fast car," "extremely rare," "extremely beautiful woman"... they all bring images of second mortgages, and in the case of the latter, some other potentially costly trade-offs!
Flatly put,
Extreme accuracy OOTB is costly. If you really want it, get a Jarrett or other custom. That Tikka which is so highly regarded is a good choice at around $600. Before optics, secure transport case, ammo, benchrest gear....
However, better than adequate accuracy is easily gotten from names like Savage, Remington, Winchester, Browning...well, you get the idea. And as a reloader, you can work up loads that will be as accurate as possible in any given gun.
Want a short list of good commercial cartridges for range shooting, for the newb reloader (component selection) and which may be used to take up to deer-sized game?
.243/6MM Rem
6.5 x 55 Swedish
7 x 57 Mauser
7mm-08
.308/30-06
There are others to be sure, this is just off the top of my head. Youll notice that 3 of 5 are milsurp rounds as well. However let me add one caveat:
Dont shoot commercial hunting rounds in milsurp guns much, if at all. Milsurp is invariably loaded to goodly lower pressures than the commercial stuff.
Best value for the dollar? Savage. But then, we dont know what you're calling a "budget."