I suppose I'm a couple years late to the party, but here I am, beginning my journey through UF.
I was on TV Tropes the other day, looking for some kind of crossover media to endulge in, be it official or fan made. From there, I came upon the page for this, and the description for it sounded like something I needed in my life.
I just finished the first story earlier today, and have started on the second. It's a bit weird to read, but I am enjoying it, and can assume that it keeps getting better. I'm not super familiar with Dirty Pair, Bubblegum Crisis, or any of the other series that have been mentioned so far, but the explanations have been good enough so far that I don't think it matters too much yet.

So, from what I've read around, it is recommended that I read the four core stories before anything else? Or should I read any other stories in between? After the four core stories, should I proceed to read everything in chronological order, or release order, or some other order? Are there any stories that should be skipped, or should I read everything?