I wonder if we could persuade the NFL to move to 18 games with only 2 preaseason games. We could then do two conferences with two divisions with two subdivisions in each. The two division winners would go to the playoffs, and winning the subdivision would be the first tiebreaker in case of any ties. It wouldn't guarantee you the playoffs, though.
As to the schedule, it would be:
6 games that are against your subdivision (home/away)
4 games that are against the other subdivision in your division
4 games that are against one of the two other subdivisions in your conference (rotating every other year)
4 games that are against one of the subdivisions in the other conference (rotating every 4 years)
I think that might be my ideal setup, at least until the NFL moves to 36 teams. Unfortunately, the reality is probably that we'll move to 34 teams by the end of the decade and to 36 by the middle of the next decade. The best situation then probably becomes:
2 conferences with 3 divisions of 6 teams with 16 games.
10 games home/away
3 games against the (upper/lower) half of the division you're matched up with in your own conference (rotating every other year)
3 games against the (upper/lower) half of the division you're matched up with in the other conference (rotating every 3 years)
By upper/lower half, I mean that the top 3 teams the prior year would play the top 3 teams from the other division and that the bottom 3 teams the prior year would play the bottom 3 teams from the other division. I don't particularly like the loss of predictability in terms of interdivision and interconference matchup frequency, but there isn't much else to suggest.