Lots of opinions on this matter.... I shoot a Weatherby. because I like the best.
Remington is a very nice gun... always has been always will be. You could never go wrong with a remington.
I am not familiar with the Savage but my brother-in-law shoots one... he loves it.

IMO a .270 is a great deer caliber. But then again so is a .30-06, 308, 7mm mag.. etc....

Get what you like... all are great guns and will kill deer.
Good luck!