The 7mm/08 might give you a little more range and accuracy. But the .308 Winchester is a very accurate round with a very good bullet selection.
If all you were going to hunt was whitetail deer, I would say that the .308 is all the more you would need.
If you also wanted to shoot woodchucks and small mammals, the 7mm/08 would be a better all around choice.
Both of them kick about the same amount on that gun platform ( model 7 Remington ). I have shot several 7mm/08's that were on the edge of brutal, and I hunt with a .300 Winchester Magnum - Browning Pump Rifle, which is a much heavier rifle and absorbs the recoil much better than the Model 7.
As for a scope, I always buy the best that my budget allows. I stay away from them $100 or less scopes.
Leupold, Bushnell, Nikon are all good manufacturers.
Get the highest power scope you can buy, along with the largest objective.
I have a 5 x 15 x 50 Elite 3200 Bushnell on my .300 Winchester Mag and I have a 5 x 15 x 40 - 3200 Elite on my .270 WSM Browning A bolt Medallion. Both will shoot the middle out of a 1 inch bulls eye, all day at 200 yards with the right load.
The A Bolt had a Leupold scope on it when I bought it that was only 3 x 9 x 40- ( Vari X I ), and was too dark and too small a magnification for what I use it for.
All the deer I shot this year was with one shot to the neck, they only went 3 feet - straight down!
