I wouldn't say any of those options.
I'm British and I would play for the soccer team (well the football team, but I'm not going to quibble about that).
I'm British and I would play for the soccer team (well the football team, but I'm not going to quibble about that).
And yes, they should have used 'football', and let each locality think they meant a different sport :)
It can be really confusing when all three are somewhat popular in one country.
I'd call rugby league "footy", but rugby union will always be "ruggers".
Playing for the team suggests that I'm part of that team. Playing with the team would say to me that I'm not part of them, but I've been co-opted for a game or something like that.
Oddly, I would say "playing with the orchestra" rather than "playing for ...".