Pretty much any bolt rifle in any caliber you want .243 or bigger. Remington 700 is a classic. I love my browning a-bolt. Savage make a veryaccurate rifle for the money. Tikka's are deadly accurate, even if they have too much palstic for my taste. I even hear pretty good things about the newer Mossberg and Marlin bolt actions that are very affordable. Do not get a Remington 710, or a 770. Any of these will be a huge jump in performance from your old 35 remmy. Be sure to save a few hundred bucks for the scope.

+1 on the latest hottest new caliber, 308 marlin might not be around in 5 years, along with most of the wsm and wssm's. The 300wsm seems safe, others not so much.