One thing you'll run into (literally) is eye relief on inexpensive scopes on a 300 ultra. I've used both Millet 4-16 and 6-25 and Mueller 8-32s. I think the Mueller has better optics, pretty even otherwise.
I think you would be better served by something from a better brand, leupold vx-I, nikon buckmaster, etc.
I'd also buy used. Check out lots of forums, samplelist.com, and put up a 'want to buy' ad.
good luck.