I wouldn't put any more than a 2X7 on your Winchester, maybe even look at a 1.5X5 size. If you do any woods walking, and need a quick sight picture, the last thing you need is a lot of power on the low end of your scope. I'd look really hard at the Burris Fullfield II, Bushnell 3200, and the Weaver V7, all in 2X7X32, all are in the $150~175 range. I have a Browning BLR in .308 that I put a Leupold VXII 2X7X33 (out of your price range,$299) on and it is about a perfect fit for a quick handling rifle. Bare minimum would be a Bushnell Trophy 2X7, at around $100, and on the other end you can get a Leupold VXI 2X7 for around $199. You'll find out that you'll only need the higher end of your scope when you're sighting it in or playing at the range, but when you're hunting you'll keep it cranked down to the minimum, so you can find your target quickly as it comes bouncing in front of you. If you could find a retailer that has a large selection to look at, compare them and see which one gives you the quickest, clearest sight picture when you draw it up to your eye, and I'll be you'll come away with a good scope. If it were me I'd just buy the least expensive Leupold I could afford, and never look back. They have always been quickest and clearest to my eye, even the VXI and the Rifleman's Ive looked at.