The Cosby Show was easily the best 80s family sitcom. Family Ties was probably the next best, but I think the humor was more suited for the Reagan era.

Most family sitcoms were pretty episodic and you could watch any episode or miss any episode without losing much, so there's not really one you'd need to "commit to." Maybe Google the top 10 episodes of several sitcoms and watch those rather than try to binge whole series from start to finish like we often do nowadays.

If you want to watch one from start to finish, I think Roseanne had a bit more arc and character development over time, but I never saw the last few seasons, which I've heard were pretty bad.