Automatic offsite backup services like Crashplan, Mozy, Carbonite etc ensures your data will survive both media failure, theft and fire. You may also choose to keep a local copy of your media, because downloading hundreds of gigs over the net takes a while. But: I'd first put my money into one of these providers, and if I felt I still have too much money then I'd consider a NAS/Time Capsule kinda solution as a supplement.
And never, ever, ever exclusively store data you care about on DVDs and external hard drives.
For the first time in history, our pictures and videos can live forever - completely without quality degradation. It's amazing. And it's disappointing how few people take opportunity of this.
(Of course, you should take care to double-check your new computer can play back whatever media formats you have used - and convert if necessary. )