Synology NAS here. Currently an 1813+ as the main device, but as long as it’s DSM they are all the same.
I have all the shares setup as AFP and SMB shares, I don’t use NFS – just prefer SMB as it works cross platform, although these days I don’t think it makes a bit of difference. AFP I avoid as it was too buggy, and again struggled across platforms.
For mapping of drives, OSX always used to struggle to auto map like windows so you had to mount each time. I wrote scripts for each of the fileshares, each time the mac boots it finds the drives (one Media, one Software, one Backups).
For my Air I don’t keep much on it, but backup important files. iTunes accesses all media from the NAS, and Plex library from the NAS. I use Rsync to backup each time I start up on the local network for all regular documents. It replicates all that is on my Air to a NAS replica.
I follow the same principle for other machines, the Pro has more backed up but it’s just a backup. The Mini is a media machine and is used for BluRay rips, each night it looks for new rips that have appeared, copies to the NAS and deletes of the machine.
The NAS is the main hub, and operates as file shares for all media and files that can be shared, this means I can get to all software and media, with all music appearing to the amps in each room, all TV’s run plex so can stream movies and TV from a single source. Far simpler.
For any files (music, docs, whatever) that you want to replicate a copy to the Mac, just mount the drive and use Rsync. If you don’t like the rsync interface, then search for a tool called BackupList+, it’s an automator for Rsync it works really well.
Once you have everything setup you can add Time Machine to the NAS as it’s useful backup, or if all is synced to the NAS Time Backup is useful for a time machine like backup so you can prevent numpty file deletes. Obviously this is space dependant so bit the bullet and chuck a couple of high capacity drives in there.