I tend to play like I learned in online leagues. I sim about a week at a time.
I do not stop the sim when a player comes off the DL. If a player is injured for more than 2 weeks I stop the sim.
Solo I let the AI handle lineups in Majors and Minors.
I run through my messages at the end of each sim. Pull a player off the Dl or throw one on.
I check the leader boards about once a month.
The draft and free agency are my favorite parts of the season. I take that back, the playoffs are better.

If we make it.
I do not make trades I think are bad for the AI teams.
I am usually exhausted when I sit down to play and need to unwind from life, I prefer a pretty passive experience.
Online I am a co-commissioner in the league I am in. Run sims 1-3 times a week. That is a much more interactive experiece, I am far more invested than in a solo league.
Good luck,
Tom