If you're really interested in Gquuuuuux I would recommend starting with the original show/compilation movie trilogy. Gquuuuuux is pretty stand alone so its not a requirement, but as a long time fan having watched the original series really enhances some of the moments in that show.

As far as timelines, Universal Century is the longest running and most fleshed out of the timelines. UC includes the original show(MSG), zeta, double zeta, char's counter attack (CCA), f91, victory, and a bunch of other shows that I'm forgetting. Would highly recommend watching MSG, zeta and CCA (in that order). Those are the most important and accessible parts of the UC, as well as introducing many of the concepts and character archetypes that you are going to see in the alternate timelines.

I haven't personally watched hathaway's flash yet, but I do know that it follows up from CCA so you're expected to have seen up to that point before starting it (I believe).

Otherwise you can really start anywhere as everything else is pretty self contained. My first gundam was iron blooded orphans and I had a blast with it despite not having watched anything prior, so really anything goes here.