You're going to spend some money on a decent tape drive, but adding storage (media) is an incremental cost, and, as you've read, properly handled and stored tape has a great archival storage lifetime. Tape-based backup systems work very well if it's well managed and maintained. Tape is expensive, and I've love to see a hard disk based system that is supported by a name-brand manufacturer, has a comparable cost-per-GB of tape to add more storage medias, and is as durable as tape media. RDX is close, but the cost-per-GB is outrageous in comparison to tape.
Think about the data you're protecting and what it's "worth". That should help cushion the blow re: the expense of a tape backup solution. Be sure to amortize the cost of the solution over the intended operational life time (I'd recommend a manufacturer's service contract on the tape drive for the intended operational lifetime, as well). Per month, per GB, it's not as expensive as you'd think, and it's certain to be less costly than data loss (losing track of who owes your firm money, who you own money, and potentially going out of business... no fun).
I wrote a little comparison here last year comparing some different backup technologies. Depending on how you project growth of your data, you're probably somewhere in the multiple LTO-3 or single LTO-4 tape per-full-backup range.
If you haven't read The Tao of Backup. It's an ad, but it still says a lot of good things.
Learn about the terminology associated with backup-- full, differential, incremental, copy, etc. I won't rehash all thsoe here. The Wikipedia article on Backup does a pretty decent job,
Things you need to consider:
What's your backup window-- i.e. in what hours can you take a backup w/o worry that files will be changing during the backup? You need to choose a backup solution that is fast enough to perform the backup in the time you have allotted. (Sometimes a disk-to-disk-to-tape strategy is employed if the window is very short because disk-to-disk can be much faster than disk-to-tape, and after the disk-to-disk backup is completed the production systems are left unencumbered while the secondary disk-to-tape backup completes).
How often do you need a full backup to take off-site? You can do full backups less frequently if you use differential (or, ugh, incremental) backups in combination with regular full backups. You typically would do this if your backup window is longer over, say, a weekend, but shorter during the week (since a full backup takes longer than a differential or incremental backup).
What's your projected data growth? This helps you size a backup solution that will last for your intended operational lifetime. A standalone tape drive is mechanically less complex (and likely less failure-prone) than an autoloader, for example, but if your projected growth would exceed the capacity of a single tape per backup then a standalone tape drive wouldn't be a good choice for automated backup (since someone will have to change tapes during the backup).
How many backups do you want to retain off-site? Typically you'll retain some "window" of off-site backups such that you can recall data from weeks, months, or years prior. This will influence how many tape medias you'll need to buy, and should be factored into your cost planning. This might also influence the type of off-site storage location you use if you're talking about a lot of medias.
Do you need tape-based encryption? Remember that the tape, by definition, has all your data on it. If you don't encrypt it then you really need to treat it very, very carefully.
There are lots of tape backup management programs out there. For a NAS device like the one you describe, you're probably safe using any backup management program that can handle connecting to the file sharing protocols that the NAS provides (SMB, NFS, etc). Personally, I'm an adherent to the Symantec Backup Exec religion, but there are others out there. (I wouldn't recommend the CA ArcServe program to my worst enemy, though...)
I think that LTO is the only tape "game in town" anymore. SDLT tapes have been fragile in my experience. VXA tape drives have suffered mechanical issues at a couple of my Customer sites where we tried to use them. LTO has just worked and worked for us. I have a particular affinity for the Quantum SuperLoader autoloader devices, but I've used Dell and HP-branded devices with success, too.
A possible disadvantage to LTO (particularly LTO-4) is that the drive needs to be fed data at a fairly constant clip or you will have very sub-optimal performance. If you don't feed data to an LTO drive fast enough it will "shoe shine": the tape will stop, rewind, and pickup writing again. LTO-4 is particularly susceptible because it's very high-throughput, but the older LTO tapes will "shoe shine" if not fed fast enough, too. This need for high-throughput means that LTO tape drives will need SCSI / SAS or fibre channel connectivity in order to function effectively. If you can't feed data to the drive fast enough over your Ethernet then you may need to do a disk-to-disk-to-tape style backup to get the data copied from the slower-than-necessary Ethernet to a disk array locally attached to the server computer hosting the tape drive that can feed the data to the drive fast enough not to "shoe shine".
Ill-managed tape is failure prone and costly. Be sure that someone is monitoring the backups (preferrably with email notification). Be sure that tape rotations are happening. I recommend keeping a paper-based log of the tape rotation and preferrably rotating it off-site with the tapes. It's very nice to know which tapes are the most current after the building burns down w/o spending hours "cataloging" every tape in off-site storage.
Don't get fancy with your backup system. It should be as simple as possible, and you regularly test restores to be sure that you're really getting what you think you are. Nobody does backup to "do backup"-- you really want restore capability.