I think... well, all of it's extremely important. As an intense competitive smasher, i have the desire to see lots of balance, a very similar engine to SSBM, and could really care less about the items. I want balanced stages, and as anybody who knows me can tell you, a near obsessive desire to play as Meta-Knight from the Kirby games.
But since it's produced to a much bigger audience then the hardcore, I'm also expecting and hoping for frenetic levels, ridiculous items, and tons of chaos. Because I'll not just be playing this game one on one, but I plan to invest in a lot of free for all craziness on and offline.
Of course, there's online play... just as long as the means through which it's achieved is good, I'm happy. Decent channels for searching, and customizable game search settings (much like filters for online games) so you can set things to "item settings: on, off," stage. If I had to guess, it'll probably, for online play, be done that way, with the "host" of each game picking everything, everybody saying "we're ready" and then hitting start or whatever. It has always seemed just like the most efficient means of handling those things in an online environment, because the way the game is now with everybody being able to fiddle with controls and settings, the general *******ery of the internet would come into play IMMEDIATELY and we'd be screwed.
And lots of single player stuff. Crazy gimmicky things so that people who don't take the game seriously can still find a ton of things to enjoy about it without having to play tons of crazies online.
The thing that gets me still about online play is how people can just quit during matches, which is blah. And as other people have said, lag is my biggest worry. That's why, basically, I picked "whateva," since all those elements will be dead important to making this game a commercial success like its predecessor.