Caliber isn't really an issue when it comes down to the price of the rifle, but it does play a part in ammunition. For 1k you can get set up with a 270 Win, 7mm mag, 30-06, or 300 Win Mag. I would stay away from short mags if you don't reload, as they can be significantly more expensive to shoot. If you haven't shot much it would be wise to stat away from the magnums to help make sure you don't develop a flinch, as a well placed shot trumps magnumitis.

You would be better off spending 5-800 on a rifle and 2-500 on a scope and shoot a bunch than you would if you dropped 2x that much money on the gun and only shot 20-30 rounds per year.

If elk are in your plans I recommend getting something with a good quality synthetic stock, not the cheap plastic handles found on many rifles today(meaning buy a rifle with a cheap stock and put a Bell & Carlson medalist or H-S Precision on it or just get something with a sturdy stock). Savages and a Remington 700 SPS are good but stocks are probably flimsy(can't speak for the Savage) or Weatherby Vanguard Sub MOA which has a good stock. Elk hunting takes place in unforgiving environments, and while a wood stock looks much better, they tend to warp and swell when they get wet, no sense in buying a pretty rifle if it loses zero middle of a hunt and you can't make the 1 shot you are presented with. A stainless rifle is nice but not necessary, the advantage that I have found with stainless is on a multiple day hunt in wet weather, you don't have to break it down at night to dry it off to keep rust at bay, just put some electricians tape over the muzzle to keep the bore dry and worry about drying it off and getting rid of any rust after the hunt which would be minimal.

Also, stay away from scopes with too high a magnification. Nothing worse than seeing a big bull at 30 yds and having too much magnification. A 2-7x40 or 3-9x40 Nikon,Burris, or Leupold will do everything you need and last you many years. A 50 mm objective gathers more light, but adds weight and can make proper scope/eye alignment difficult.