Between these 3 models, I would choose the Savage or Ruger, with Ruger probably being a smoother action gun. I own Savage and Ruger in smaller calibers and Ruger's just have much smoother actions, but the price difference was also there.
As to a deer caliber. You can use anything from 243 up to 30-06 to keep the ammo cheaper and finding it on virtually any Mom-n-Pop shelf anywhere you travel in hunting areas.
I'd say the Savage Axis or the Marlin XL7. Each are very good rifles.
Ruger lost all of my business on their rifles years ago.Their accuracy is hit or miss,and the triggers are probably the worst in the gun industry.They all require gunsmithing to be good shooters.
And run as fast as you can away from the Remington 770,it's a piece of junk from the start.
I own two Remington 770 30-06 &243 love the accuracy detachable box magazine. The action is cheap feeling and don't like the stock much I am left handed and the cheek piece is on the wrong side but for under $300 what do you expect?