Pick up a Surgeon 591 short action repeater and bring it to me along with $1850 and I'll turn it into the baddest .308win you've ever pulled the trigger on!
I havent shot the axis, but i know it doesnt have the accutrigger. If you lookk you should be able to find a used one with an accutrigger around 500. I think some of the ones that walmart sells have the accutrigger.
500 Is just a little shy of some really great rifles on the market. If you could bump your price range up just to around 550- 600 , you could get yourself a really great rifle like an SPS , Savage hunter , or a Tikka T3.
If you ever plan to later do upgrades the Rem 700 has more aftermarket parts than any other option. If you are going to keep it stock the Savage is probably the best bang for the buck.