So, a few things.

[@DisguisedDemon], you as a GM should stick with whatever Gundam setting you know best/feel more comfortable running this in. Me? I'm mostly a UC guy, just because of the wealth of content to it, but there's plenty of room to run stories in other universes. I don't particularly like CE, but it's the one where third parties have shown to have the most freedom what with the multiple mercenary groups running around and independent orgs having very, very advanced mobile suits and pretty much personal armies to their name. You pick what works for you, because the guy running the game should probably feel comfortable doing so.

Gundams are Gundams, but remember that the piling of sidestories have made them not terribly unique in most universes. Better than most, sure, but hardly one of a kind. There's several mass production or limited production Gundam-types in UC, they're just a high performance unit with a V-Fin on and there's many nongundams with just as good performance. It should be less about "pick and choose who gets gundams" and more "are you making Gundams the be-all end-all or are you actually allowing non-Gundams to compete?". A level playing field for the PCs should be more important than what you call each robot.

Finally, an idea for a setting that affords plenty of independence from the Federation and Zeon both while keeping them extremely important: make a slight AU where you extend the three way conflict at the end of the Gryps War, keep the factions from both Zeta and ZZ and make the AEUG the player faction. AEUG are the moderates composed of both earthnoids and spacenoids, they're probably the single most sensible group that wants positive change for everyone and tries to achieve it without resorting to extremes and causing mass loss of life and permanent damage to the planet. At the same time, they're an extremely irregular force that recruits all kinds of people from all walks of life.

The Titans being around means there's plenty of people unwilling to work for the Federation, but many still see the Titans as a necessary evil to counter the rising Axis Zeon which actually drops a colony on Earth. Axis has some legitimacy as a followup to the Zabi regime, but many spacenoids don't want yet another warmongering dictatorship. You also have Anaheim Electronics selling stuff to everyone and making a killing out of it all and a time period that's a sweet spot for high performance MS development with a lot of neat gimmicks without getting into full on Newtype Magic like CCA and Unicorn.

tldr: Work with what you know and would be most comfortable running, a level playing field for the PCs is more important than whether they call their robots Gundam and a setting idea.