Of the three cartridges you mention, the .30-06 is the most versatile. The .270 is a great deer cartridge, though. And I consider the .300 Mag overkill for whitetail. Remington 700s are great guns; same can be said of most of the Savage line. My personal preference is for Remington.
Note, though, that there are several short-action cartridges that are also fine deer rounds, including .243 Win, 7mm-08, and .308. Despite being over six feet tall, I prefer a shorter, carbine-length deer rifle for hunting the hills of Pennsylvania. I settled on a Remington Model Seven in .308; my son hunts with a Model Seven in .243. Both have taken their share of deer.
So a lot depends on the terrain you will be hunting. If taking long shots from a stand over fields, I'd favor the ballistics of the .243 or the .270, and length or weight of rifle matters less. If hiking hills and woods, I'd favor a short-action cartridge in a carbine-length rifle.
Oh, and look for a copy of the book, The Rifles, the Cartridges, and the Game, by Clay Harvey. It's out of print, I believe, but available used from Amazon.com. Excellent discussion of different cartridges for different game animals, and the various rifles available at the time of printing. Very good discussion of why one might choose one cartridge/rifle combination over another.