My first thought was a savage or a weatherby vanguard in 22-250 or .243 (if deer is ever in the equation) topped with a burris ffII 4-14x42 with ballistic plex and a harris bipod. Scope could also be a Bushnell 3200 or 4200, Nikon Monarch, or a used Leupold or Ziess. I would go 3-9x40 with a sporter barrel and 4-12 or 4-14 with a heavier contour barrel. If you plan on shooting a lot and ranges will be no more than 300 yds on game, a .223 might be the one you like.
Rifle $400-500 with tax, shipping, etc
Scope $200-350
Mounts $50
Bipod $50-75
Sling $25
Equals $725-1000