Why do you want a .243? Deer also? Why not a .223? That's what I'd get if its just for varmints. Ammo is cheaper and you can shoot more with the .223.
I have a Rem 700 in 7mm-08 and its pretty accurate, like 1-1.5 MOA with Rem 100gr Corelokts.
Savages have a good reputation for accuracy. I don't own one, however, but if/when I get a bolt specifically for varmints, Savage will definitely be on the short list.