SQL Server engine in one place with database files on NAS
To be honest, I wouldn't want my database on a NAS as it is most likely accessed throughout the office and it is also very vulnerable as everyone connects to it. Ideally, your SQL database should be hidden in the deepest parts of your network. 

However, I seeing how this doesn't sound like a high end operation, I would see if they can give you the money to get a desktop and install SQL express there to run the database for them. That way all of your clients can just connect to that server from within the network and you have a central point to pull backups from.