We ran an 18 team league last year on
http://www.myfantasyleague.com. Just as stated above, we set it up as 2 different conferences of 9 teams apiece. Each conference drafted from their own player pool, so no one ended up with John Beck as their starting QB.
We
DID play inter-conference games, so there were no teams that had to have BYE weeks. The issue of two players going against each other was something people worried about at first, but it ended up being no big deal. The 2 teams in the superbowl had no overlapping players.
We set the league up like this:
Conference 1 - Divsion A: 5 Teams
Conference 1 - Divsion B: 4 Teams
Conference 2 - Divsion A: 5 Teams
Conference 2 - Divsion B: 4 Teams
3 teams from each conference made the playoffs, with highest seeded team in each conference getting a 1st round playoff BYE.