Your rifle and caliber will enable 1000 yard hunting capability. Base capability for a scope that balances well with your choice of rifle/caliber would be:
5x20 power range
Side parallax adjustment
Turrets/ 30mm tube for sufficient elevation range
A crosshair that includes a MOA horizontal graduations for windage holds, vertical graduations will be determined by whether you want to use reticule holds with a calibrated reticle.
Some decision points will be:
Use of turrets or Reticle holds for elevation adjustment at distance.
If turrets, choice of MOA or yardage,
Your budget is suffucient to get a solid scope. Don't think you could go wrong with a Nightforce NXS, Leupold MK4, or Huskemaw
, just to name a few. I have used all three with good success. It is at the high end or may cost a little more than your budget, but the Nightforce NXS 5.5x22 with an MOA reticle is probably the standard by which most scopes are judged for LRH.