First, let's clear up a big misconception.
RAID is not a backup! RAID is for redundancy (or speed if you use RAID 0, though that's actually not very good unless you use SSDs). If you have a bunch of files which absolutely need to be available any moment of the day for your business to keep operating, you want RAID. That way if a hard drive dies,
your business can still continue to function as if nothing was wrong. Pick up a new hard drive from Frys, pop it in, rebuild, and you're protected again. But your business never suffers any downtime due to the dead drive. (Do note that with modern TB hard drives and rebuild times, most people now recommend two-drive redundancy (e.g. RAID 6) instead of one-drive redundancy (RAID 1, RAID 5). With one-drive redundancy, if another drive fails during rebuild, you lose the array.)
The reason RAID sucks as a backup is because you can immediately and irrevocably erase files. You accidentally deleted a file you needed from your laptop, so you find it on your RAID file server. Just as you're trying to copy it, your cat jumps on your keyboard and deletes it. You are screwed. File recovery programs won't work because it was stored in some weird RAID format, not FAT or NTFS. A backup should be something you write to
and never erase until the drive is full and you're ready to make new backup images. Ideally you'd be using write-once media like DVD-R, but those aren't big enough now so most people just use hard drives and live with the risk of accidental erasure.
In this respect, your current two-drive backup system is better than a RAID 1. If your cat jumps on your keyboard and deletes the file from your RAID 1 file server,
both copies of the file on the two drives get erased simultaneously and you are screwed. With two separate drives, if the cat erases the file from one drive, you can still recover it from the second drive. If all your backups fit onto a 2TB drive, I would recommend continuing to backup as you are now onto two separate drives. If backup time and space are an issue, I'd recommend looking into incremental backup programs like Easeus and Paragon Backup and Recovery. They will backup only the changed files or changes to files, instead of everything.
A NAS is really for if you want a central file repository simultaneously accessible by multiple computers, without having to burn 100 Watts keeping a computer on all the time. The cheap ones will only manage about 20-30 MB/sec over gigabit ethernet - no better than your USB 2.0 external drive. To get decent performance (50+ MB/s), you should expect to pay $300-$500 or more. Basically the same as a new small computer, because that's what they are. These are real-world performance figures. The cheap ones can manage 50+ MB/s on sequential read/writes, while the expensive ones can manage 90+ MB/s. But in real-world use with mixed small and large files, 20-30 MB/s for a cheap NAS and 50-60 MB/s for an expensive NAS are more realistic. In particular, the D-Link 320 you listed tops out at about 20 MB/s sequential read/writes, which is pretty abysmal.
Since the NAS is always on, it's possible to automate backups to the NAS. That's what I do. I have scripts running on 3 computers which automatically do incremental backups to the NAS every day. This is the main advantage I can think of for a NAS over external USB drives in your case. But I then backup my NAS to a multi-drive USB media bay ever couple weeks. Just like RAID is not a backup, a NAS is not a backup!
If you do want to go the NAS route, I'd recommend researching on this site:
http://www.smallnetbuilder.com/nas/nas-reviews
Don't expect performance if you go cheap (I ended up just building my own using a low-power CPU). And remember, even if you have a NAS, you will still want to back it up. It may be easier because you're now backing up one NAS instead of two laptops (the two laptops backing up to the NAS automatically). But you still want to backup the NAS.