Here's how I approach every playoff. I root for my favorite team as long as they are playing. Then I move on to my next favorite team that is in the playoffs.
In order:
Buffalo
Montreal
Ottawa
Tampa Bay
Vancouver
After that - I have favorites that I don't follow as actively so I'll pick one of Chicago, Minnesota, Detroit several others.
Teams I won't ever root for - Boston, Rangers, Kings, Ducks, Philadelphia, Carolina, Florida, Dallas, Arizona