Do you have a computer that you can spare? If so, just a basic windows comp with PhotoSync companion and PhotoSync app on both iOS and Android. The apps can be scheduled to do nightly backup to your comp. PhotoSync has a one time payment plan and it has been working great for me. You can only view the photos and videos as files not as photo albums like on immich but for simple backup it is great

I think that's a great way to start. It is surprisingly easy to add remote access at a later date.

The dead simple way is to set up a shared folder with Syncthing, although you will end up with all of the files copied onto every device.

If you want the files to live on your home server to be accessed as needed, then you will want something like Nextcloud or OwnCloud. Personally I found ownCloud easier to set up, but it has far fewer features.

If the focus is on pictures and videos, then you should probably start with immich. It is very simple and incredibly powerful. You can more or less set it up once, and not think about it too much other than running an update from time to time. It supports multiple users, etc. Note that if you are adding photos from a Google Takeout, you will want to run a one time script to rescue the metadata (date, etc.)

Any of these are accessible on any device.

First you need to specify a bit more on what you mean by file server. Are you looking for a network attached storage for home use, or remote use as well? Or are you talking something like a seed box for torrenting Etc. What general software environment will you be working with and what others are you comfortable with.