#1. NVIDIA makes the GeForce line of GPUS and then licenses the technology out.
#2. ATI makes the Radeon line of GPUS and either makes it themselves or licenses it out
#3. Matrox makes 3D rendering cards and is not intended for the consumer use but rather the programmers and web design geeks.
#4. it depends on you needs. my rule of thumb:
Basic: GeForcefx 5200 or GeForce4 Ti4200, the latter being better.
Mainstream: GeForceFX 5700 Ultra, Radeon 9600XT, or GeForceFX 5900XT
Performance: GeForceFX 5900(ultra) or Radeon 9800(pro)
eXtreme: GeForceFX 5950 Ultra or Radeon 9800XT
i prefer the ati cards listed for the above categories, but i hear the fx5900xt is solid bang for the buck.
i made assumptons u have a decent system (ie. 1.5ghz, agp 8x, 256mb ram), anything less performance will be bottlenecked and should look for the radeon 9100 or geforce4 mx440