I just got a Winchester Model 70 Coyote in .270 WSM and its a good all around long range hunting rig. Shoots really accurately especially for a pretty much factory rifle, and was reasonably priced. Its built on the Winchester model 70 CRPF action(matte blued), has a heavy stainless 24" barrel, and a laminated stock with wide fore-end(great for sandbags, bipod, shooting out of a deer blind). It may be alittle higher than something like a Savage, but its alittle less than a Win Stealth or Rem Sendero and(although they have some strong supporters) I would never put savage up against a Win model 70 or Rem 700 for quality. You can get a coyote in any of the WSM calibers and I think the WSSM calibers as well as some standard short actions like 22-250 and .308.
It will have a really heavy trigger out of the boxso take it to a gunsmith (you could actualy do this yourself) and have him clean up the trigger and take it down to 2-2.5 lbs. for probably less than 50 bucks. Also have him check that the barrel is floating and if it touches anywhere(mine did alittle bit directly below the barrel about halfway from the front of the reciever to the tip of the stock), go ahead and have him fully float the barrel and reseal the stock where he removed wood. This should also be very cheap of you could do it yourself. I think i actually spent 50 total for the trigger and floating work at a local gunsmith. Then you will have a good shooting rig. I just used a standard 2 piece leupold base with leupold rings(i think around 40 bucks for both). I dont know why people are all about thier hardcore ultra heavy duty scope mounting hardware with the rail and the huge rings, its expensive, ads alot of weight, and unless you beat the crap out of your rifle or are looking for any edge you can get for competition, i think youll be fine with the regular leupold mounts. Ive always used them and dont believe theyve ever moved on me.
That should leave you a couple hundred bucks under your 1000 dollar cap for the scope. If you have enough left over, get a 3.5-10x40 Leupold vari-X III. The Vari-X III is a good scope and i dont know that you can get better without dishing out a bunch of money for the european optics. If you dont wanna spend that much, a 3-9x40 or 4-12x40 vari-X II should be fine(i think you can get the 3-9 for just a couple hundred).
That will get you started and I think will get you in the best possible setup for the money. It should do all you want it to. After you get more money saved up you can get some dies and reloading stuff to start handloading your own ammo which will be cheaper and higher quality. Then get other accessories like Harris Bipod(a definate must) and you can upgrade stuff on the rifle as wanted when you can afford it(full pillar bedding job, lap lugsinto full contact, muzzle brake
Hope this helps.