Wow that's a lot. I have PC, PS3 and PS4. Don't mind the atmosphere or anime tropes, I'll go wherever the fiction takes me. Pure VNs are basically glorified text adventures right? I played a lot of text adventures back in the day so pure VNs should be fine too. I've role-played as women in Bioware RPGs so romance isn't a problem.
I'm really confused as to how the anime fit in with the games.
Uhhh well then I think Steins;Gate would be a decent place to start. It's great but it takes a while before it really gets going and your mileage may vary on whether you enjoy the characters (including the protagonist) before that point. I enjoyed them from the start but that's reasonably not true for everyone, particularly as they lean into tropes pretty hard (for a good reason, but still).
Beyond that The House in Fata Morgana's fantastic, though the first part of it might be a little offputting given that it's not particularly clear where it's going at first.
Maybe it's bad to start with the best but you might as well go for them if you're not looking for anything specific. And for what it's worth, Steins;Gate took me 40-50 hours and Fata took me about 30.
(Without a Vita the romance thing matters a little less and if you have no real preference most of the rest didn't matter either, hah.)
And as for the anime- do you mean Steins;Gate specifically? It just adapts the game. If you mean in general, it's just that some characters lean into the tropes as I said.