One comment on the scope you choose- I'd get a variable for that range. It would allow you to zoom in on a target or have some field of view on lower power. 10x has little FOV at the lesser ranges you mentioned. The Leupold scoeps are great, just keep in mind that the factory mildot is only accurate for range estimation at the higher power. I believe the Premier Reticles offers a first focal plane mildot that stay accurate at any magnification. (I've got a SS10x42 on my 10FP and it's too much power. I shot a whitetail last year at 110 yards and the whole deer just barrel was in the FOV.)
On rifles, one thing to say about Savages vs. Remmy's is Savages are NOT being out shot by Remmy's. The barrels as of late on Remmys have been questionable. If you're o.k. with replacing it to see an accuracy improvement, then Savage has the Remmy beat as well, since a home gunsmith can easily swap Savage barrels, and Lilja and Doulgas tubes are both available prethreaded and fully chambered. Can't do that with a Remmy.
The squaring of the action on a Savage is not necessary due the the way that the bolt meshes with the barrel. It can be improved but only a little and isn't necessary.
The plus's for the Remmy are aftermarket parts, but that has become a smaller advantage as of late.
For the 700 Milspec, check out snipershide for more info. That have been touted to not be anything special for a couple hundred over a regular PSS. for that matter the PSS can easily be outdone by buying a short action remmy, swapping out the barrel for a quality one and a better stock.
Which ever way you go, you should be able to get a fine rifle for under $1500 with scope.
If your want to try a Savage out, let me know. I've got a nice shooting 10FP.