Most NAS's are real servers, running a form of Windows or an embedded Linux :-)
Sounds like you're looking for general CIFS support and the ability to add storage. Since you have a backup solution in place, I'd consider getting a beige box with several large drives in it and running something like FreeNAS to configure with RAID. Shouldn't be too hard to get increased storage capacity from that and it will be compatible with anything that can mount Windows shares, and you can administer it from a web page.
The server itself will be immune to common viruses. You should still run something on the clients to check that there aren't viruses on the shares, though. I don't remember if FreeNAS has the ability to run Clamscan or not. On the plus side, a generic system running FreeNAS should be inexpensive and easy to get parts for.
If you don't have budgeting concerns I'd otherwise look at a Dell NAS. Our system is a little on the older side, but it's basically a Windows appliance, and you can install an antivirus of choice on it.
At any rate keep in mind what RAID you want to use and get a decent network card. You don't say what kind of files are copied to and from it, but if they're big, you'll want to use a RAID level and disk controller (and drives) that can handle high speed transfers. It's not hard for a NAS to get overwhelmed with several large data requests if the network is a gig in speed and the drives aren't high-quality and high speed.