Clerkship: anything federal...possibly a state supreme court in Oregon or Washington
Clerkships are an odd bird, and your successes will often depend on a lot of intangible factors (such as, well, luck). That being said, grades are the strongest indicator of whether you'll get a clerkship or not. Its hard to pin down actual chances, but suffice to say that Chicago does better than almost any other school in terms of clerkship placement.
State Supreme, on the other hand, is significantly easier coming out of Chicago. But I think a strong requirement for those is a connection to the state in question.
Govt: FBI/CIA/DHS/DOJ - I'm interested in anything relating to national security or intelligence.
I can't speak about the FBI, CIA, or DHS (although I do have a couple classmates who worked at DHS prior to coming to law school), but we have a great track record when it comes to the DOJ, both for career attorneys and for political appointees.
Firms: DC, Virginia, North Carolina, Oregon, Washington
The only market I can speak for is DC, which is where I'm heading.
DC is one of the grade-snobbiest markets out there, but there are also a lot of firms. And very few of them have been hit hard by the current economic situation (if anything, I'd say work has picked up at DC firms). I know this year students didn't seem to have any problems with DC. And while I can't speak for everyone, I was really happy with how my OCI process came out.
Sorry for the lack of details, but its hard to answer general questions like this.