I don't think I have any singular approach to how I root for a team, or, what is most important. It depends on the situation.
Championships are inportant, but not at the expense of discarding thos who got you there previously like yesterday's trash. Guys like Antoine, who never truly won anything here, I can deal with moving on from.
I don't need my teams to win the title every year. I do need them to care, be enjoyable to watch, and prefer them to be competetive (or making progress towards it). Sometimes those desires run in oppostion to loyalty, in which case, as I said above, depends on the players and how worthy of my loyalty I find them to be.