The NFL schedule complicates this matter further. Here is a skeleton schedule for each team;

• You play each divisional team twice (4 team divisions, 6 games total)
• You play each team in another division in your conference (4 games)
• You play each team in a division of the other conference (4 games)
• You play the teams who had equal finishes in their division in your conference last year. For example, last year Indianapolis, New England, Pittsburgh, and Kansas City came in first in their divisions, so they will play each other this year. That makes up the remaining two games.

Therefore, you would need to spread your team purchases throughout the divisions in both conferences in order to ensure that you have access to all of the games. I suspect that you would need to buy at least 3 teams from each division to ensure that you would get all of the matchups (since buying two teams from each division will ensure that you miss the interdivision matches between the teams you don't have). My guess would be that the minimum would be 24 teams then.

[EDIT] Actually, the more I think about it. You need to buy all 4 teams in at least half of the divisions, since the cross divisional play requires playing all of the teams in the opposing division. Therefore, if you are missing a team in each division you will miss their game with each other. That makes the minimum 28 teams to ensure that you catch each match.