My priorities for online SSBB in descending importance:
1. Minimal lag. Looking at their track record, I'm assuming that Nintendo's got this covered.
2. Matchmaking without friend codes. Random and rivals is fine (for this stage). Random matches are very likely.
3. Customization. Either that or make the default 4-stock 1v1 without items (something that I highly doubt Nintendo would do). This is the one that I'm most concerned about. Look at MPH, SMSC, MKDS, etc. None of them have customization for online modes (unless you're playing someone on your friends list). Actually, if we're going to petition for anything, this should be it.
4. Non-random matchmaking. Setting up your game in a game room would be nice. This could also work with #3.
5. A way to prevent people from using Action Replay or similar programs.
6. Interaction with other players. If this happens, it'll most likely be limited to people on your friends list.
7. Rankings