Only 180GB of anime? Come back to me when you've got over 1TB, we can talk about storage, backup, and restoration solutions then.
(Protip: RAID6.)
ETA: 1 double-sided dual-layer DVD = 17GB = 15.9GiB (a little over that, actually, but not a significant amount enough to matter). So he'd need at least 10 double-sided dual-layer DVDs to store all of that anime, and it wouldn't be playable as a DVD because hey guess what, DVD can't into 720p/1080p/mkv (which is what most quality releases are, nowadays).
ETA2L Also, DSDLDVD are pretty rare. Most common DVDs (e.g., the kind you can buy in spindles of 25-50 discs) are DVD +/- (R)W, and are single-sided, which brings you down to ~9GB storage (and half again if it's single-layer as well).
-- Griffinhart