In general (IMHO) it’s best to use “good” all-quads topology up until you have a specific reason not to (like converting to trigons to do some game optimization). I’ll almost always use a Cap Fill Type of Nothing or (rarely) Triangle Fan, and then use a Grid Fill in the center much like you’re showing (I use the Simple Blending, I’m happier with the quads off of the N-poles).
I won’t say it’s impossible to UV unwrap and/or texture trigons (I’ve done it) or n-gons, but I’ve had fewer glitches with quads.