Can I use Simpletest to test site upgrades? Going through upgrades it's often a bit tedious to test site functionality such as creating and editing nodes. Can Simpletest perform this kind of functionality? Or do I need a solution like Selenium?
It depends of your Simpletest tests. Upgrade your site in a test environment (stagging ideally) and then run your Simpletest tests. If tests are ok you can be sure that everything covered by your tests is ok.

If your question is if Simpletest can create nodes, yes, it can. What Simpletest can't do is test Javascript. If you need to test Javascript you should use another tool like Behat. Behat is a BDD tool, so it allows you to describe the behavior of your app and test it. Behat has several drivers, one of them is the Selenium driver, that includes full JS tests (because the tests are performed by a real browser). There are otheres drivers and many posibliites.

In general Behat is better than Simpletest for integration tests, while Simpletest is better for functional testing.

If you are going to use Behat use the Behat Extension approach. Check the Drupal Behat Group too.