I also think a Savage would be hard to beat. I have a 110 in .270 that is a very accurate, no nonsense rifle. Also, have a Mossberg ATR .243 that was an inexpensive package rifle that has worked fine for me. Couple others I have experience with Ruger GSR .308 is pretty cool, if slightly non-traditional, and Rem 700 that is boringly steady. Finally, never shot one but the Ruger American has received pretty good reviews and is cheap- I guess that is a theme with me!
You can also put together an AR (6.8, 6.5, .300 Blk, etc) for pretty cheap and customize it just how you like.