I think you need to think about what you want very clearly. For example, transferring files and other data between devices screams Nextcloud. My wife and I have a local Nextcloud instance on our media center that we use to sync calendars, address books, tasks, notes, and files in general. Way useful. Some people said syncthing. My big reservation is, can you find easy to use apps (I have not though maybe they exist). The big advantage of syncthing it can do NAT traversal and you do not need any server infrastructure.

On the other hand you said you want chat. So then yes, chat sounds interesting instead, not what we do. I will leave the others to talk about chat because there are so many options and I am not a big chat guy. By the way for chat, Signal does have some sort of group chat option. That is really my only input.

I would think about where your users are. If your stuff is on your LAN, then this means a few things. First you server will not have a globally routeable IP address or domain, so every device has to be on the LAN. If for example your parents do not live with you this is kind of out. Also people talked about domain names. Domain names are not the problem. You can always put a DNS server on your LAN (often your boundary router can do this), and add your server and domain to it. What is a problem is TLS Certificates. Generally android devices have problems with non-standard CAs and probably self-signed certs. So one has to think how they are going to do that. Other option is to have a VPS at a place like Linode for example. Then your server is on the internet, but then you have to maintain it and in particular keep it patched and secured which can be challenging.

Anyway, some things I did not see others say.