how do I connect my app to firebase? Do I use the standard web JS SDK, or is there something else I should be using?

You can use standard web JS SDK as well as the react-native-firebase package.

when I was trying to add firebase to my android app on the firebase console, it mentioned adding the firebase SDK to a build.gradle file - something which my project doesn't have. So have a missed a step in my setup?

I was able to setup react-native-firebase with expo managed workflow without having to touch the native android or ios side so these steps are not required if you will be using react-native-firebase with expo managed workflow as all the native dealing will be done by expo config plugins.