I was on the same evaluation quest a few months ago and went totally off the wall and ended up with an AR-15 based varmint rifle...
However, based on my own research and handling all of the rifles in question I'd go with the Marlin X7 (XL7 long action for the 30-06 based cartridges or XS7 for the short action 308 based cartridges) given the choice of the 3 - they pack a lot of value into the price while it seems like the Savage Edge/Axis and Remington 770 are "cheap" guns skating on the well earned reputations of their well known older brothers in the 10/11 and 700 series respectively.
You might also want to look at the Stevens 200
, it's basically the Savage model 10 (and compatible with all of the same aftermarket options) without the accutrigger and, in my opinion, a much more compelling option than the Axis-Edge or Rem 770 in a new bolt action rifle vs the Marlin X7 series. They are about the same price and I don't think you could go wrong with either at this price point - the Marlin gives you more bang for the buck up front but the Stevens probably has longer legs if you're planning to add upgrades later (a stock or trigger in particular). Buy the Marlin to shoot as-is or the Stevens if you like to tinker/upgrade.
Good luck shopping and enjoy your new rifle when you get it!