I submit that testing a bunch of trivial things isn't actually going to make it easier to catch bugs. I recommend this article: http://rbcs-us.com/documents/Why-Most-Unit-Testing-is-Waste....
You can write integration tests with the same tools as unit tests.
Personally, I try to make sure all major paths are covered, but I won't test every little UI detail. It's faster to test those manually. But YMMV.