As far as a bolt .22 goes, there are lots of good options. Keeping the budget in mind a Marlin, Savage or Ruger American would work fine. Install a nikon pro staff 3-9x40 and you will have a very nice setup.
For the varmint rifle I would go with a Savage 12FV in .223 and look on Natchez for a nice Weaver scope for it or keep an eye here in the classifieds for something workable. A SS 10x would not be a bad option here either.
Big game rifle tikka in 6.5 CM or 7mm-08 or a Remington 700 in the same with a Leupold VX2 3-9 would last forever and not ever need upgraded.
I believe that could all be done for close to the budget and end up with some very nice equipment.
