Let me ask you a few questions and give some tentative answers:
What sort of conditions will you be hunting? If this is the sort of woods I frequently encounter around home, you'll be hard pressed to get a 100 yards shot. In that case, I would recommend a 1.5-4.5x scope or a 4X fixed. If you will regularly be taking 200+ yard shots, a 3-9X variable would be in order.
A 270? I 'm guessing this is a bolt gun. This is going to be the sort of bread-n-butter situation most scopes were meant for. Just make sure you give yourself the proper eye relief. When you throw your gun up with your gear on, the sight picture should be right there for you-- no head and neck adjustment necessary. Your eye should also be able to be far enough back that you don't get the scope hitting you when the rifle recoils.
My taste in scopes runs towards the penurious. I seldom pay more than $100 for a scope. There are limitations going that route, but if the scope holds together for 25 years, I'm not going to complain. Of the ones I've tried, the Bushnell Banners have been the best for consistency. I have also had a couple BSA scopes that were surprisingly good.
I had a buddy show up with a low-end Nikon last year that knocked my socks off. It was not ultra-expensive, but it did have capabilities beyond any of my scopes. When you're doing this on the cheap, you're generally going to suffer three things:
1) Durability. I had a cheap Simmons that came with KYHillChick's Savage 110 package that just flew apart one afternoon. I can't count the number of Tasco's I've seen do the same. If I take in a rifle in that has a Tasco, I take it off immediately.
2) Low-Light problems. Early in the morning and late at night, on the edge of legal hunting is when you see if you have a good scope or not. My best Bushnell Banner, although it works great every other time, gives me mush in low light. It cuts off about 10 minutes either side of legal hunting. My buddy's Nikon was wonderful in this regard. The night he brought it out, there was a fellow over on the next ridge trying unsuccessfully to drive his truck out of the bottoms. We cranked the Nikon all the way and rested it against one of the pillars on the front porch and it was like we were there. I brought out my scope, and all we could see was the lights.
3) Overall clarity. Remember, you're looking through slabs of baked sand. Some scopes demonstrate this more than others. Usually, one peak through the scope in the store will tell you if this is going to be a problem.