Regular MAME is what it is. As for the variants, I only tried a few, but the various flavors are designed to support things that vanilla MAME does not or doesn't handle well.
AdvanceMAME and a few others are geared towards using an ArcadeVGA card for an arcade monitor; SmoothMAME is good if you have a funky monitor that doesn't like odd resolutions (it runs everything at 60hz); FastMAME is heavily optimized to make almost anything run at- or as near to- full speed as possible without having to resort to heavy frameskipping; MAMEAnalog+ provides support for analog controls and some odd mouse/trackball arrangements, as well as multiple controls of the same type (2 lightguns for example). NoNameMAME is essentially all of them rolled into one program, with the result (I'm finding anyhow) that it's the most compatible and flexible of the variants.
I would try AdvanceMAME, SmoothMAME if you can compile it yourself... but NoNameMAME is my personal recommendation.
I hope this all helps, if you have specific questions related to your hardware ask, someone here will definitely have an answer.