Tapes are an older technology, generally a decently reliable technology. The biggest limitation of tapes is the amount of data that can be stored on them, as it does not compare to Harddrives, price the same. Hard drives, especially portable ones can be a viable alternative, where size will be an issue. I mean physical size, not logical size. You probably need to look at how much data you will need to back up. It may be that burning a CD or DVD will be enough. If you require more than a DVD's worth, I would definatly suggest a backup program that you can schedule. Your idea on symantec should be fine, but look at the features it offers. Unfortunatly I don't have any experience with symantec. My backup programs I wrote myself. :S
On backup plans - this should be part of your disaster recovery scheme, and the most accepted method is to have a child-parent-grandparent backup. To illustrate, the child backup might be a daily back up kept in the same room as the server that it backs up. The parent backup may be a weekly backup, taken home with you over the weekend, and the grandparent backup would be something done every two weeks or even monthly, and it would need to be in a safe deposit box in a bank. The idea being that the possibility of three catastrophies happening in three different places like that are small to none. Off site back up at least. Always Always Always have off site back up. Even if you put it on a tape and drive it to the bank every friday @ noon.
That's kinda my take on it.