Athlon is a brand of chip, AMD is the maker. If you want a budget system for gaming then I suggest getting something like the 35w 2400+ XP-M if you're intereseted in overclocking and a good suitable OC'ing board like the ABit NF7-S v2 it's a very popular combo, either that CPU or the 2600+ XP-M which are mobile chips, but they are Socket A and will fit in a desktop socket A mother board, They have great overclockability and it's easy to get them to 3200+ XP speeds and past or at the very least give you a 400FSB.
As far as what card goes with what processor, well it really doesn't matter, the cards made to go with either system so you can't really say nvidia goes with amd and ati goes with intel or anything like that. Personally I like nvidia and right now think they are on top of their game with the eVGA brand 6800GT 256mb, you can OC that up to and past 6800Ultra speeds.
For the most part people generally agree, AMD = Gaming, Intel = applications because AMD performs more cycles per clock than Intel due to short stocky pipelines whereas Intels are huge in comparison.