Don't waste your money with the really cheap ones, you'll end up taking them back. The good ones work well. When you buy a 2x lens, you're paying for the glass quality. Higher price, clearer glass, better picture.
Which lens you buy has nothing to do with how hard it is to stabilize... how far you're zoomed in DOES. If you get the lens, you'll be able to zoom in twice as close so it'll be twice as hard to stabilize.
The cheap Century brand lens is not worth the money, you'll take it back. Everything I've bought from them I've sent back. Tiffen makes good stuff..