Probably the Independents because they are easy going and can sell any of the basics (i.e., all weapons, all ships aside from special elite variants like XIV).
As for ships and weapons, that is a hard call. For frigates, I like high-tech best. For destroyers, I like Medusa best for flagship but prefer Enforcers for AI. For cruisers, it is Dominator or any midline (Falcon, Eagle, and Heron). For capitals, I prefer Paragon, but Onslaught will do in a pinch.
For weapons, only Tri-Tachyon sells heavy blasters in sufficient quantity. However, Hegemony has lots of military markets, and can get unusual stuff from time to time.
Currently, of the majors, Hegemony because they control the most systems and markets. They are also pragmatic and not too evil. If Tri-Tachyon (or the other majors for that matter) had more accessible systems and markets, I would consider them, or at least Tri-Tachyon.