Hey James,
I have tried updating everything, including Modules, Themes and Core, and eventually many things did broke.
I did that by updating the Core first, check on the release notes and any major changes, that will impact my custom code or contributed modules settings.
If things break now, Dont panic, you might find many modules which will work only after specific version of drupal core, because of a bug fix.
Next, you can start updating your modules one by one, recommended, and see what version of module is compatible with which one. Also there might be a complete new version of module available, which might not work for you, something like from 7.x-1.x to 7.x-2.x, which is ideally not recommended, you should upgrade within the same version.