I play in spectator mode, and just follow my league.
I usually watch 2 games a day, one AL, one NL, for the most part. It's a 36 team expanded MLB with all fictional players. I get to know who's who in the zoo pretty quickly this way. I pick teams at random to watch, maybe a team on a hot streak, or one where a player has a chance for a record or career achievement.
I watch every play off game, all star game and usually in Sept I watch more games. Pennant races are fun, and division rivalry games are always fun to watch.