Say you're looking at the 6 basic types of UML diagram (from this The Elements Of UML 2.0 Style)
Pretend you're insane and you feel like drawing up all 6 diagrams for your system.
Which would you start with? Then which would you go to? What's the best order to visit each diagram if you have a pretty clear idea of what you want your system to do?
I think you should start with the physical diagram and work your way to class diagram. Top down, I always say..? Am I wrong?
Use cases are the main ones that define "what" your system does, possibly followed by state machines and activity diagrams (which could be seen either way -- normally the activity diagrams are more about the "what" and the state machines more about the "how", but I've seen counterexamples to each); class and sequence diagrams, and even more so component and deployment ones (collectively the "physical"), are more and more about how your system does what it does. I'd definitely go from the "what" towards the "how" as the reverse sequence makes little sense -- how can "how" make sense if you haven't defined the "what"?
So, summarizing, roughly: use cases, activity, state machine, class, sequence, component, deployment. This order makes sense because it gets deeper towards the implementation aspects and away from the analysis aspects, so e.g. somebody interested in understanding exactly what use cases you'll cater to and what business rules you'll apply (activity diagrams) may stop "reading" earlier than somebody who needs to understand the full detailed logic of your deployment strategy.