Imo, it'd have to be 8 way movement, And perhaps a Standard and Special attack. The SSB Formula could work well.
I don't think you'd even have to send that info. Basically I think you could get away with just sending what's being pressed and the other calc would control that character on its process with those key presses as though they're playing on the same calc. The only issue could come from if there's either differences in timing, lag, or random number generation. Or at least that's how I'm seeing it.