I like all varieties of RPGs and will try them all even if the story sucks, the battle system is super complex, or easy to the point of no challenge just as long as either the story or battles are good. I also enjoy third person shooters, mecha sims such as Armored Core, and some dating simulations.
I like RPGs the most because a good RPG can keep me entertained throughout.
Must feature -
-Compelling protagonist (unlike TWEWY IMO)
-Excellent backstory and plot
-Engaging Gameplay with some strategy, not just like err.. a hack and slash where attributes don't even matter. Even Mario and Luigi RPG 3 had strategy.
A bonus is fanf*c*ingtastic graphics like these FF remakes on DS or Fable 2 and Oblivion.
PS: I don't really understand "Fighting (Hack and slash/ beat em up)". Where do you leave Street Fighter, for example, then? It's neither "hack and slash" (like Golden Axe) nor a beat'em up (like Streets of Rage). Nevertheless, I'd apply the term "hack and slash" to RPGs mainly, and to some action-adventure games like Zelda, not to a "beat'em up" or "brawler".