For your stated purpose, I'd scratch the 300 off of the list. Too much unnecessary recoil for deer sized and smaller targets. The 7mm has a better bullet selection than the 270, but the 270 will offer enough flavors to get by, so flip a coin. Over all,for your purposes, I'd lean towards the 270, just to be kind to my aging shoulder.
Of course, I'm too slow-witted to actually take it easy on my shoulder, so I'm holding out for the .325 WSM. It sounds like a nicely balanced medium bore, although it would be far too much for varmint shooting.