Back in 2008, when I had my Amiga3000UX still, I had setup an NFS network with a Debian GNU/Linux server running as the NFS server and I ran AmiTCP with an NFS client which allowed remote volume mounting.
Probably easier for the UNIX nerd than Samba, but I've used Samba before and it performs acceptably, if noticeably slower than NFS. There are three problems I can see with using NFS:
You will need a UNIX, BSD or GNU/Linux server, which if you're only used to AmigaOS and Windows, then its going to be a rough road.
Windows XP I remember I was never able to get NFS working properly and securely. Dunno if this plagues Windows 7+
NFSv3 was what I used which, if you don't use a VPN, can be quite insecure for your network as anyone with the same UID you set as the owner of the NFS share can mount and modify your files.
For backups, I manually compressed copies of files for the 3000 I wanted to preserve then dropped it on the NFS share. Probably some sort of cron system for AmigaOS that can do the commands automatically.