A human has about 4 billion base pairs, which are roughly 2 bits each, so that is 500 MB. You could fit that on a CDROM with room to spare. But humans share 99% of their DNA, so you would really only need to store the diffs. 1% is 5 MB.
A copy of the (haploid) reference genome encoded as 2 bits per base pair comes in at about 800MB:
Run that through something like Z-zip and you can store it in less that 640MB, so it will indeed fit on a CD. Each of us has a diploid genome, though (a copy from each parent), so you really need to store double that if you take no account of the high level of similarity between both copies. If we assume a known reference genome, however, the 'diffs' are as you suggest very small - one paper reports compression down to 4MB, small enough to email:
Lots of analyses are done with lists of variants with respect to a reference genome, but the raw data generally comes from 'next generation sequencing' platforms, where every base needs to be sequenced many times over before bases can be called confidently, and quality scores of base calls need to be stored. The raw data usually needs to be kept since alignment and variant calling algorithms are improving all the time. Storage requirements are something like 80GB+ compressed.