I really don't understand self inserts. I am myself all of the time. Games/books/movies or whatever give me relief from me. Lol. Plus it's weird to think that it's me romancing the pixels? Idk.
I am a writer, however, so I think of my pcs as characters to be written with movements and dialogue.
I'll play either, though DAI has given me the most reason to switch it up and play as a man (hello dorian).
That's pretty much me and my response (except I'm male). It largely depends on the game and lore mostly. I never make any character remotely like me (I'm far too boring and I'd be freaked out playing someone who looks like me). I play all genders, races, and sexual orientations. I'll be the first to admit a male character in an m/m romance feels natural, but I have zero problem making a character outside that, and in fact most of my characters are outside that.
In Dragon Age, I'm completely fine playing as either given the world itself is very heavy with female leads/important characters (Cassandra, Leliana, Morrigan, Flemeth, etc...are far more impactful than Alistair, Loghain, even if male characters have a presence the females often outshine them). My Wardens and Inquisitors are pretty much 50-50 but I'll admit to preferring male Hawke over female Hawke. Nothing against voice or anything else I just happen to like Hawke as a man better.
Mass Effect I'll admit I strongly prefer male over female characters. My 'main/original' is female, but Shepard's animations and design are much more geared for a male character. Though I admit I do like Jennifer Hale's voice a lot.
Elder Scrolls games I can go either way. It really depends on the character type and even personal headcanon/neo-universe story I'm telling (I tend to create several characters per neo-verse).
Diablo 3 I preferred female characters because most of the male characters were hideous. I had a male Demon Hunter and Wizard since they looked good but the rest were female since the males were unbearably old, gnarled and ugly.
MMOs I prefer female because they tend to look much better. Males are either too action figurey (DC Universe Online/Champions Online, guilty as charged) or females just happen to have cooler designs in general (many of the Asian MMOs).
Just my 0.02