Any help would be greatly appreciated.
I think that the 30.06 is probably the most common caliber around here (Rockies), followed maybe by 308. 7mm Mag and 300Win Mag are right up there too. I have always used Remington 700, and I am extremely biased in favor of it - Mostly 30.06 and 7mm Mag, but in recent years, I went to 300Win Mag. In the common market, in commonly available calibers, you'd be hard put to find a better rifle for stopping power at long range... Which is why I have it... But any of the above mentioned calibers should serve your purpose, and should be readily available, at least in the West.
My current Remington 700 300Win Mag w/ Shepherd P1 scope was purchased used and un-papered for a combined $450... which is well within your price point. If you have a handful of Benjamins and wait for the deal, it can happen.