I like 14. The best record in each conference gets the bye, everyone else has to play. Then you're just adding one more team in each conference. Lets the league go 1:00/4:30/8:00 on the first weekend.
I don't like 16 teams because then the top seeds have to play in the 1st round, and they would be upset too often for my liking, just due to the nature of football.
I like 14 because it adds meaning to having the best regular season record. The only change from 12 to 14 is that the 2nd best team in each conference no longer gets a bye. Let's not act like it would be a huge change.
16 would be a huge change, because it would eliminate 1st round byes and necessitate either playing 1st round games on Friday or Monday, or starting the early games at 10 or 11AM on Saturday and Sunday. Playing on Friday or Monday creates advantages and disadvantages for round 2. Starting games in the morning would screw with gameday routines, and you don't want to be messing around with that stuff during the playoffs.