Yes, volumes with individual permissions is common practice with NAS and servers. Similar to sharing a drive on your Mac. Most NASs and Servers let you set up a volume of certain size on a larger disk and then set permissions. You enter a list of users and then go to the volume and add/subtract/change users.
Most NASs speak in Unix type language/terms, however. If you aren't familiar with Unix, thats the hardest part. Once you get used to the terms, its not so bad.
If you want even more protection, the user can set up encryption on all or part of a volume. Useful when there are several users and you don't want the admin reading your files.
If you want to use the NAS as a time machine destination, then look for NASs that are approved by Apple (I don't think there are any besides TimeCapsules, AEBS, or another mac). Many here set up a server on a mini or a retired Mac and attach a hard drive. Its a real computer so it gives you more flexibility, scalability and performance for just a little more money. I grew out of a NAS in a year or two, if I had it to do over again I'd go right to a mini server.