You can definitely use Nvidia cards on an AMD CPU. The reverse is also true - you can use a non-AMD GPU on an AMD CPU.
For $100, there isn't much you can get, though knowing what your needs are will help. Are you intending on gaming, video editing, or just web browsing? The earlier in that list, the more powerful the card you'll need to get to make the most out of it. The 6770, if you can find a deal, is probably the best you're going to find with your budget. For video editing, you should consider an Nvidia card due to cuda support. The 550 Ti is about the closest you'll be able to get. For just web browsing, then pretty much any video card will do.