Howdy and welcome to the forums, Barry!

I agree with pretty much everything everyone else has said on the board. The .270 vs. 7mm vs. 30-06 debate has raged on for years, and will probably continue to be argued for years to come. Any of them will serve most people well. And both the Savage and Remington are fine arms that would serve you well. Like others have mentioned, your hunting success depends on your weakest link. Don't let it be your optics. If your going to skimp, skimp on the rifle and not the scope. I would also recommend a good set of binoculars. When stalking and scanning, good binoculars are worth their weight in gold. I've known some people that don't carry binoculars, they look through their riflescopes. Bigtime safety issue IMHO, because the rifle looks where the scope looks.

As far as hunting techniques, study the animals you plan to hunt, and know their habitat, food, habits, etc. Always be aware of the wind, and use it in your favor. Camoflauge color isn't a big factor, but how well it breaks up your outline is. Most game animals are active during the early morning/late afternoon hours, so I find the first few minutes during sunrise and the final minutes during sunset to be the most important.

Good luck and good hunting.