1, 3, 6, 4, 5 in that order.

1,2,4,5

1 is first because of time constraints 3,4,6,7 are all pretty equal for me.

I'm with MojorDespair on this and for the same reason.  I need to be able to save and resume a game later when I have time again so 99% of the time playing is spent VS computer.  After that, I play the odd game against a friend.  

So, for me:

1,2

3, 4, 6, 7, 2, 5 in that order 

Here are my answers to your question on game modes:

Most important will be Free for all (3 players or more)

Second most Important 3 humans vs. 3 humans

Third most important Skirmish games vs AI

It really depends on what mood i'm in.  I like the competitive aspects of 1v1, but some days you just want to grind vs AI and relax for a bit.

I prefer when I get people I know to all play on the same side vs a bunch of AIs. I'm not a huge fan of competive multiplayer with people I don't know but I if I know someone that is about equal to me, it could be fun, or maybe there should be a handycap system...

I would play multiplier verses humans if there's a ranking system in place.  I'm not one for just sitting in a lobby and eventually someone joins only to get smashed in 30 secs by someone with more spare time than me.  sup com fa did this ranking system well.  I also liked the 4 vs 4 because again there was labeled games novice intermediate expert etc and you had 3 others to back you up.  

Otherwise i I just play me verses ai hard / very hard when I bet that I play me verses 2 when I beat that it's me verses 3 and so on so on.  If the mates are free then and have the time for a full game then it's coop verses ai.   Me and the mates just don't  do verses each other matches ..mates want to do coop or team stuff Not kill each other.

if we are talking modes, I still think specific premade scenarios against the ai would be cool.  especially if they where deliberately made to be as hard as possible and not easy to complete like single player always is.  Scenarios so hard they come with a disclaimer if you loose forever, talk to the hand because the face ain't listening .. The krogoth encounter on the ta expansion pack springs to mind.  I remember us all coming to school and all talking about whether we have completed the krogoth encounter yet ... One single mission verses the ai became the only thing played by many for weeks.. 

For me:

1,3,5,2

I really like the single players missions where you have to fight a overwelming force and slowly get in a better position.

1,2,3,6

in no particular order, also like outnumbered in example fighting 2v3 against the computers or against 2 friends.

1, 2 and 5