Per Webopedia, a chipset is a number of integrated circuits designed to perform one or more related functions.
If you're referring to an NForce(Nvidia) chipset on a MB, then it will work with an ATI video card.
ATI makes very good performing video cards. The model that you need depends on your usage, i.e., are you a hardcore gamer who likes to play the latest state-of-the-art games, do you do a lot of video editing, are you into graphic designing, or do you want to use multiple monitors, etc., etc.
WRT CPU selection, AMD makes excellent performing CPU's that are less expensive than Pentiums, but they do run a little hotter so you have to get a heatsink, fan, and case that are designed to provide adequate cooling.