I first try to get through my unreads. I usually work my way up from the bottom, because the ones on top seem likely to be most active, and I figure I can dispose of the ones at the bottom without having to return. I do about three tabs at a time, clicking through them, closing them, and then opening new ones. There is also usually a separate tab open for PMs.
If I have the idea that something major is happening in a thread in which I have not previously posted, I check last 200. I also use last 200 on the rare occasions that I make it through my unreads.