Well, its just my personal preference, but I'd buy a savage over the other two makes because its cheaper and shoots just as well (if not s kosh better) I get half inch groups out of my savage 116 in 30-06
. But really, you can get a stainless savage 116 short action for $50-100 cheaper than a remmington or winchester or ruger if you shop smart. The triggers on savage rifle tend to be heavy (as is true with most new rifles these days) but you can guarantee under 1 inch groups.
Remmington makes a fine rifle and there is less "slop" (side to side up and down movement) in the bolt than on a savage when you cycle the action. Remmington's open sights are excellent if you don't plan to scope the rifle. Remmington also still makes the "carbine" length model 7 which is very handy in the brush.
Winchester (some but not all of them) has a mauser style action which snaps the cartridge into the bolt face and CONTROLS the feed into the breech. In this way you cannot stove pipe 2 cartridges into the breech like you can on "pusher" acions on the savage and remmington. If you buy a winchester make sure it has "controlled round feeding" Its usually easy to tell as the long mauser style locking lug rides down the right side of the bolt. Winchesters also have 3 position safties which is a nice feature.
I should mention Ruger here too, because they make the model 77 "international " in 308 full a full length mannlicher stock that is gorgeous and lightwieght (i think is has a 20 inch barrel). Rugers also use "pusher" actions in their model 77 rifles. The ruger has the MOST "bolt slop" of all the above rifles, but also one of the better triggers. Rugers are usually reasonably priced as well.
Really if you shoot them all equally well... go to the shop and see which one "fits" you the best. Take a long hard look at fit and finish, ergonomics and handling, and of course price.
For my money that's been the savage , but for yours it may be another make.
my two cents,
Dr.Rob