*checks spiral notebooks*
Yup, sounds right to me.
Having set up a precision rifle myself, with advice from here, I was reasonably certain the P-F cognoscenti "school house" answer went something like this...
Rifles:
Ruger American whatever - best pick for budget conscious, while still delivering a solid platform that will punch above its weight class
Tikka CTR, Bergara B-14 HMR, Ruger Precision Rifle - all very solid performers, with a slight edge to the Tikka for smooth action. Then again, the Bergara fits into Remington footprints, which can be nice. Pick whichever you like - they'll all outshoot the nut behind the trigger
Scopes
Leupold, Vortex - folks have their favorites, but both are more than adequate for what most people will ever use them for. Slight edge to Vortex on basis of price. Athlon scopes also worth looking into. Remember, Schmidt and Bender is just German for "couldn't swing the Hensoldt"
Double-checking your stated budget, you'd be hard pressed to go wrong or be unhappy with the Ruger American Hunter + whatever Vortex glass you like. Tough as nails and more than capable of putting accurate rounds on target a serious ways off.
Best wishes in your search. Cheers!