I'm far from being an expert so will relay only what works for me. The problem breaks down into at least two domains: Organization and Backup.
The simplest is backup. There are a plethora of backup and copy programs which can be automated and scheduled so that you need remember to do more than periodically check that they are still working. I use two: SecondCopy and AISBackup. Why Two? for the same reason that you use two disks - the same gremlin probably won't get both. I use SecondCopy to back up specific folders to various media during the course of the day (it's optimized for this) and AISBackup to do daily and weekly global backups. Both are shareware and of minimal cost.
Organization is a much more touchy/feely beast. Generally, the number of opinions on the best way to organize is equal to about 1.5 times the number of people discussing it. I use subject oriented folders and the occasional keyword for the moment. I've discovered that the optimal organization evolves over time so that one's software needs to be very flexible. For example, I've just added RAW files to the mix so now I've got the whole problem of RAWS, Backup RAWS, edited TIFFs or PSDs and JPGs used for uploads and mailings in addition to the original, in-process, and finished (editing) states folders.
Dates don't work for me because much comes through my scanner and the dates have little to do with actual image dates which are usually about 30 - 60 years prior. Subject works until something fits in multiple categories. I don't have clients or job numbers so that all escapes my view. I use ThumbsPlus as my organizer. I find Bridge to be not quickly flexible - change your mind on category names and groupings and you might as well start over. Have no experience with Lightroom or Aperture but many like them.
Lastly, I'll suggest that you migrate your DVDs to USB drives and use DVD as your last ditch medium. You can grab a 1 TB USB drive and run with it in a matter of seconds. DVDs fail often and easily and are not suited to automated backups. It's coming up on that once a year that I burn a spindle of DVDs to leave at someone's house