Of the ones on chess.com, I would have to say crazyhouse. Drops definitely provide a lot of edge-of-your seat action, and now is a better time than ever for people to get into it due to more and more resources cropping up. Unfortunately there's no readily available and feasible sets to play OTB, but I think that crazyhouse has become its own thing as more of an internet-oriented chess game.
Outside of chess.com - I've got a fair bit of experience playing many weird and wonderful different games, but one that I have began to study as of late is shogi (Japanese chess).
Disregarding the language barrier, shogi is nearly flawless - it may be slower than chess in design but that's how it's meant to be played. And with drops, the draw rate is under 2% among top-level players. At lower levels it's non-existent. I could blab about how it teaches you patience through drops and reservation of material gain, but really all chess variants develop these same skills. However, someone said to me a while ago that playing shogi can improve your bughouse tactics. I can't say for certain if that's true, but by all means you should definitely give it a shot.
What is your favorite variant? like mine is bughouse