As VRStu mentioned, Synology is a very good NAS. QNAP also make good boxes. The beauty with these is that even though they may cost slightly more, they can do a lot. You can use them as iTunes servers, web hosts, DLNA servers, even set up a surveillance system by adding IP CCTV cameras! You can access them both locally and remotely etc.
These units come with both USb and eSATA ports in the back. If you fall short of space you can add additional external drives to the unit for more storage space. Or you can add external HDDs ( or even another NAS) to the unit for backups.
Backups on these can be incremental if you wish. You can either have the Backup drive keep an exact copy of what's on your NAS at all times, or you can set it so that even if you delete something from the NAS it will not be deleted from the Backup drive at all. Either way, you can schedule the backups to occur as often as you wish, so they just happen in the background without you having to do anything at all. When you append to a backup, which is what I do, it simply backups up only the changes that have been made, so it's almost like synchronising with the master copy on your NAS.
Failing that, you could always go for a full on network server instead. I have some for sale over on the selling section
