Widget vs Unit
These are very similar in the way you think about them (you can even have them in the same file). You want to test small individual parts of widgets just as you do during unit tests.
All Unit and Widget tests will run blazingly fast so don't shy away from writing a lot of tests! The main difference with Unit and Widget tests is the WidgetTester object. This object will let you interact with the widgets and well as create them. Luckily in the integration tests, the syntax will be pretty much identical as during the widget tests so get familiar with this object!