• Your user account on GrapheneOS is just a local user account
• GrapheneOS comes with its own camera, gallery, contacts, sms, phone, and file manager apps, a hardened fork of Chromium called Vanadium, and an app that lets you install sandboxed versions of google play services and google play store, if you so wish. Nothing else. You can install other apps using F-Droid, or by installing the google play store app.
• GrapheneOS does not have a “cloud”, aside from the web services it uses to check for and pull new updates. If you want to sync files somewhere, you can install whatever you want (Nextcloud, Google Drive, etc)
• F-Droid is a fine choice, and the google play store is as well, all depending on what your priorities are for your phone. I only use F-Droid and have no non-foss apps on my phone for privacy reasons, for example.
• Running your own Nextcloud server is a great learning exercise, but it’s a big commitment of time if you’re not already familiar with linux administration, and if you want it to be secure and accessible remotely that’s even harder. Don’t let that be an impediment to getting a secure phone though - you can always keep using Google Drive for now, and then learn how to set up Nextcloud or some such as you go along.

Good luck!