If you manage aggro, you only need ~400dps tank, except for the Angel Bonus room.
You need a minimum of 300dps to complete a L4, but that will be painfully slow. Shoot for around a 600dps tank if you're a beginner, then just go for all-out applied damage.
EHP doesn't matter in missions, since you shouldn't be fitting extenders/plates.
Both passive and active shield tanks work. Drakes, Rattlesnakes, and the occasional Rokh can passive tank fine. Ravens (as well as each version of their hulls), Tengus, and Maelstroms are famous for dominating L4s for shield pilots.
Browse loadouts tbh.