The Fate/ franchise has been around long enough that I'm not sure it's even possible to avoid spoilers anymore. The recent releases seem to be skimming through the exposition a bit, assuming that the audience is already familiar with the background material.
I expect you're going to miss some references (and encounter some spoilers) whichever series you start with. I liked /Zero better than /stay night[unlimited blade works], for what it's worth.
I'm liking GATE as of episode 2; it seems to be doing a reasonably realistic portrayal of battle between a medieval army and modern military. I do hope there's a decent plot twist in the next couple episodes, though. It's starting out a little predictable.
Knowing what's ahead, it should get better. I'm surprised by how boring they are making the first few episodes. The reason why it feels so slow is that, considering the manga, they just spent 2 episodes on only 2 chapters. That horrendously slow. I was looking forward to this anime but I can't say it's incredible up to now.
Gangsta is looking like it might be pretty good. A couple of "handymen" act as hired muscle in a city plagued with corruption and violence. It reminds me of Black Lagoon, in both style and subject matter. Interestingly, one of the protagonists is deaf, and communicates via sign-language/lip reading. It actually has me wishing I understood some sign-language. I mean, that had to be expensive to animate.
I'm pleasantly surprised by this one too.