Since data on the site has a tendency to fluctuate often, what kind of stuff should I do to set up my tests? Should I some of the methods test against my own account and hope the expected results don't change?

If you have a good design (buzzword: dependency injection) you could use Mock-objects for your test-cases that replace the classes that do the actual network-access and return defined test-data.

In this way the tests for your "business logic" do not break when a site changes.

Test::MockObject can help a lot for such things.