I start with Unread Posts (that's what is bookmarked). I use lots and lots of open tabs, both for threads I've posted in and threads I just read for pleasure.
Then, I'll open Unread Replies and see what moved past Page 1 of Unread Posts that I need to read. I then am annoyed that I ever posted in certain threads, but never just unread. I might just open and close, though.
Then, I go through the pages of Unread Posts from the oldest to the newest, because that usually makes it the quickest, as I don't care about most older threads.
Whew! I'm exhausted. I need a beverage.