First of all, congratulations on moving up to 12 Teams from 10. Everyone in your League will benefit from this, as position economies neccessitate more strategy in the draft, waiver wire, trades and starting lineups. You'll all become better players for it. Right on.
I'm in several 12 team Leagues:
3 Divisions of 4 Teams Each - The three Division Winners make the playoffs, and anywhere from 1-3 additional teams. My personal preference is that 4 Teams make the playoffs (Div Winners plus 1 WC), as to some effect it leaves marginal teams out of the playoffs. Your WC team could be either the non-Division Winner with the best record OR the team that scores the most points, if it's not one of the Division Winners - it's up to you.
4 Divisions of 3 Teams Each - The League I'm in that uses this format splits the Divisions into 2 Conferences. Each Conference has 2 3-Team Divisions. Division Winners get automatic berths, and the next best team in each Conference by Record and Points Scored makes it as WC Teams. I like this format a lot. The two 'best' Division Winners get byes, and the 'lesser' Division Winners play the WC teams in the first playoff round...you can make it more interesting by making the WC from 'Conference A' play the 'lesser' Division Winner from 'Conference B', and vice versa...or you could go with just the 4 Division Winners making the playoffs, if you choose...
2 Divisions of 6 Teams Each - Division Winners and next 'best' 2-4 Teams make the playoffs, depending on the League.
I, too, am a strong proponent of less than half the teams making the playoffs. Whether it's 4 or 5, you have to draw the line somewhere between the men and the boys...
Regardless of which format you choose, if you have WC teams, I'm a strong proponent of allowing the team with the MOST points scored, REGARDLESS OF RECORD be one of them, if he doesn't get an automatic Division Winner berth...W-L records sometimes aren't reflective of the 'best' teams...there's no question in my mind that the team that scored the most points is a strong team worthy of having a crack at the postseason...
Now, in the local high-stakes 12 Team League I run, 6 teams make the Postseason Tournament. This is because with so much money involved, people get a little bit salty about it being less inclusive. However, I model our Playoff Tournament after some of the National High-Stakes Leagues as follows:
The 6 Teams that make the Tournament carry their Scoring Average with them into the Tournament. Weeks 14-16, we run a 'rotisserie style' tournament, where your Weekly Scores get added successively to your Regular Season Scoring Average, for a running point total. In Week 17, it's back to Head-to-Head, 1 vs 2, 3 vs 4, 5 vs 6, each game playing for a different cash payout.
Some might like this, some not. I think it eliminates a lot of the luck associated with 6 teams making the playoffs, and the two truly best teams compete for the top prize. My guys are all vets, and understand the nuances of the system. They set themselves up during the draft, and during the season, to have squads that cover the contingencies of the Week 17 Championship Round...
...just something else to consider...