Fighting games are probably my favorite, though I haven't spent as much time with them due to having a terrible computer and not having the right consoles.
Shoot-em-ups would maybe come after that, but I don't practice those enough, and a potentially 20+ minute session being totally ruined by a mistake or few can get annoying.
I also like platformers, though my preference is toward action platformers over puzzle platformers. I'd like to do speedruns, but I'd need to actually be able to beat the games first (and/or have more motivation).
Puzzle games can be okay, though I'd probably rather spend the time improving in something else.
I'm bad at FPSes, and if I recall correctly, dying in one shot isn't highly uncommon.
RPGs are long (so I forget the story when I stop playing for a while) and don't necessarily have active gameplay to the degree of my preferred genres.
MMOs are too liable to ruin things for people who want to play a game that getting better is most important (at least in my experience) through pay-to-win, random obtaining of characters through cash currency, and/or catering too much to casuals to the point of ruining things for those willing to try/learn.
ARPG/Hack and Slash games might have too much button mashing and/or too little depth, but I'm not actually sure I've played many of them.
I'm not good at RTS/MOBA games, since I'm not good at quickly responding to a lot of things or forming complex strategies; I typically prefer having control of only one character in real-time games, as opposed to multi-tasking.
I do not play Casual games, because they typically are not about improving your gameplay skill.
