For little more than cost of those DVDs, you can get an external drive. You can also use it for future backups down the road. DVDs are not a backup medium.
I don't understand the resistence, but do yourself a HUGE favor and worry about a backup method before making any major system changes. You'll be glad you did, and it will be well worth the money.
Honestly, I don't understand why anyone would fight such a no-brainer, simple concept. If that data is too important to be lost...then make sure it is protected.