Unless you're punching paper at 500 yrds, you don't need that kind of power. I know, I know, magnum cartridges and high power scopes are all the rage these days. How so many critters fell to a .270 with a fixed 4X I will never know...
For hunting, a 3X9X40 is a nice compromise on the rifle you described. You can get into a Weaver Grand Slam for under $300. Even the Tascos (which are now backed by Bushnell's superb warranty) are a good economy scope. You don't have to spend a lot of money if you don't want to.
Consider that at 6 power, a target at 300 yrds (prbly the outer end of your range) appears as though it were at 50 yrds to the naked eye. Can you see something at 50 yrds well enough to hit it with iron sights? Most can.
I may be a bit biased though. My varmint/predator rifles wear a 1.5X6 (my call and night rifle) & a 3X9 (my spot and stalk rifle).