It's true, this isn't your typical series. One book has a group of main characters, the next has a completely different new set. Then they split up, get back together, and what the heck's going on with the timeline?
When it comes to the main series I DO recommend publication order (that's Gardens through The Crippled God). It will make sense, it just takes a bit of time...even though it may not make complete sense - but that's just a consequence of reading the series in general. :D
With the permission of Adam Whitehead (THE Werthead) to reproduce this list he posted on a forum, below is an in depth chronological order of the entire series including novellas and Malazan Empire:
My only addition, knowledge that wasn't available at the time this list was created, is that Ian C. Esslemont's newest, Stonewielder, belongs just after Return of the Crimson Guard - at least as far as I can tell (Synopsis here).
Hope that helps clarify some things. I would use this not necessarily as a reading schedule (unless it's a reread), but as a way to wrap your head around some of the events, but of course it's up to you.
As far as storylines go, there are basically three different one's we'll call creatively 1, 2, and 3.
RG: 2 & 3
Not that some characters don't cross over into other storylines and back, but this is basically it. For TtH and DoD I'm going off hearsay.
Clear anything up? Make it more confusing? Don't even want to attempt this series anymore? I can say that it's all worth it. Each book has a stunning ending that has you salivating for more.