Tactics? Only use tactics that suit your team, e.g. don't have a 4-2-3-1 wide, if you have no wingers.
Coaches? Depends on the attributes of the coach and if you are sentimental about that
I've been sacked twice, both occasions i've taken my backroom staff with me and succeeded.
My favorite example, I destroyed everything first season as man utd as you'd expect, 2nd season i made some silly transfer mistakes and left myself short on a real goalscorer when Van persie got injured twice putting him away for 9 months!, failed to win the title, got fired, took over napoli (who lacked Cavani,Hamsik) changed the tactic to suit Napoli, won everything.