i would keep it to 3 players: enough teams and enough to make a team with 3.
For the rating, maybe it is possible to use some sort of existing
rating system. For example [en.wikipedia.org
but more simpler ones would do also of course.
And I'm in between with the 'randomizing' players. I get the point but as lno
says, you should be able to play with whoever you like. And even if it were to lead to the xuul-paars-master-rippe team, i still think there will be enough teams to give them opposition. The 3v3's are always more even (and a bit more about luck also.) Master and Harry always play 2v2 together and still people like to play with them.