In general, big stages are good because you will be able to recover no matter how far out you're thrown, and you have a lot of room to dash dance and fake out the opponent. DL64 is probably the best example of this, and is almost always banned against me when I play MK.
I actually tend to really like small stages too sometimes though, mainly because I'm a really aggressive player, and if I see someone can't handle the pressure I put on, I'll just take them to a small stage and they can't win. Yoshi's Story used to be one of my favorite stages, but now it's not even legal in a lot of rulesets, including netplay rules... I won't strike to a small stage if I'm again a big hitter like Ganon or Roy though, unless I'm going for the big plays because you CAN outpressure Ganon a lot of the time on stages like Yoshi's Story. But just in general it's better not to die at 50% and just go to a medium stage.
I will strike to a small stage if I'm against someone like Kirby or Jigglypuff though just because they have the same advantages as MK does on big stages, but they're even more annoying about it, so it's better to abuse the fact that you have more raw power than them usually.
Platforms are typically pretty important for MK's play, because you can utilize them very well due to your many jumps and they provide an escape route. I remember a long time ago there was a thread about stages where people said that FD was MK's worst stage for this reason, but I actually disagree. If you're really good at tech chasing, you can destroy people on FD, and it's really big so it provides a lot of the same advantages that a stage like DL64 provides. You will not have as many options in your dash dance and fakeout game because of the lack of platforms, but if you can adapt I don't think it's really all that bad of a stage for MK.
Just my personal opinions, would love to hear other people on this topic!