Well, the buttons are all assigned to the button with the same letter on the GC controller, so you'll have to crane your thumb around to be able to get Y and B together to run and jump (and there is at least one spot where you absolutely have to run to be able to make a jump). It's not as bad here as in Super Mario World, and you do get used to it after a while, but it's still a bit unnatural. You'll also have to memorize the buttons by name rather than by position, or the control display in battle might throw you off.
The only missable I know of is a hidden treasure chest at the beginning: the first time you're in the castle in the Mushroom Kingdom with Toad, and Toad's leading you to the throne room, run forward and jump on his head in the first, longest room, then jump onto the wall above the door. I don't think you get anything for finding all the hidden chests in the game, and I don't recall that one in particular having anything unique in it, but if you're a completionist, it'll annoy you if you don't get it, because there's absolutely no other time in the entire game that you can get it. There's probably some more missables, but that's the only one I know off the top of my head.
As for stats, every time a character levels up you get to further increase their HP, their physical attack and defense, or their magic attack and defense. Each time, one of them will provide a bigger boost than it would normally. Normally, the physical and magic boosts are only one point, so if one of them is a two or three point boost, that's the bigger one this level; if not, then HP is the bigger one. You'll probably get a feel for it after a while. You could just pick one every time if you want to try and max that stat out, but rotating and going for the biggest one will give you the most well-rounded characters.
Also, toward the beginning of the game, there will be two times when you leave the Mushroom Kingdom with your new party member (the same one both times) to go on to another area. Make sure to visit the item store before leaving both times, especially the second. If you're paying close attention to the dialogue, you'll know there's a plot device you need to pick up there. If you miss it, you'll be very confused much later on in the game (but you won't be permanently stuck or anything; just go back to the Mushroom Kingdom item store if you're at a point about halfway through the game where you can't go on). A surprisingly large portion of people completely forget this.