I know you are interested in a 4-12X but to be honest you would be much better served with a 3-9x40 in the price range you are looking at. You will get a better quality scope that will actually be clearer and brighter than what you could get with the same money in the 3-12x.

For example...
For $300 you can get a 3-9X40 Bushnell elite 4200.

To stay in the same money (actually $20 more) you would have to step down to a 3200 in a 3-12X40. It's a fine scope but it won't compare to the 4200. Until you get into Zeiss, Swarovski, etc... quality a 40mm objective lens at 12X magnification isn't going to be worth a flip in low light on a less than $300 scope.

You would be much much better off to put the money into higher quality glass instead of stronger magnification or larger lenses. You can't shoot it if you can't see it.