The Savage model 12 is an awfully good shooter for the money. I've got the 12FLVSS (no longer available) in .22-250 and aside from the plastic stock, I am very happy with it (if they had offered the BVSS in lefty when I got mine, I'd have gone for that instead).
I can't speak to the Rem 700 VLS, but I do have the 700 VSF in .308. Out past 300 yards it shoots tighter from the bench than my Savage 12. It's got an H-S Precision composite stock with aluminum bedding block. Unless you just have to have a wooden stock, consider the VSF too.
I don't have any experience with Winchesters or Rugers.