I have a Savage '06 combo package. I have to say, it's a great rifle. Mine is in '06. '06 is probably the most versitle hunting rounds out there if you stick with factory ammo. You might want to consider a .308. There are less hunting rounds available, but you can get some real cheap practice ammo since the .308 is the same thing as the 7.62 NATO. If you want to take your rifle to the range a lot you should consider the .308. If you would prefer to have a huge selection of hunting rounds go for the '06. There are plenty of hunting rounds for the .308, there are just more for the '06. As for the .300 RUM, it's more then is needed for deer and the ammo is going to cost significantly more. For example, on cheeperthandirt.com a box of Remingtom Core-Lokt 150 grain .300 RUM goes for $29.24 where '06 150 grain Core-Lokt goes for $15.52. Also consider that you can get '06 or .308 rounds just about anywhere that sells ammo. .300 RUM is going to be harder to find.
Some people don't like the trigger on the Savage but it doesn't bother me. It's heavy but very crisp. You know when it's going to go 'bang'. The scope is okay, but not that great. You can get an equivalent scope for about $25.
Another thing to consider is skipping the combo package and getting one with regular sights. Then put see-thru rings on it and mount you own scope. It'll cost a few bucks more, but then you get open sights for those quick shots that sometimes come up. Or, if you going to hunt in a wooded area where the shots are going to be 200 yards or less, you can just forget the scope. My grandfather took a deer every year in PA with a .270 without a scope. He almost invariably went for a neck shot and always put meat on the table.
As for the Remingtom 710, I've never shot one. But Remington is a good name, so it couldn't be that bad.
-This was edited to correct spelling/grammer mistakes, but I probably didn't catch them all.