RFC 1591 has this to say about .NET vs. .ORG:
NET - This domain is intended to hold only the computers of network providers, that is the NIC and NOC computers, the
administrative computers, and the network node computers. The customers of the network provider would have domain names of their own (not in the NET TLD).
ORG - This domain is intended as the miscellaneous TLD for organizations that didn't fit anywhere else. Some non- government organizations may fit here.
By this description, neither is entirely fitting for an individual or family site (it's not an organization or a network provider), but .ORG seems like the least inappropriate, anyway... it was intended as the "catch-all" for anybody who didn't fit in the other categories, though the Internet founders didn't seem to anticipate individuals rather than organizations ever getting their own domains.
Traditionally, "geek" types have tended to use .ORG for their personal sites, at least before the introduction of new TLDs. Now, I think .NAME is more logical for personal sites (if you want both a first and a last name in it, anyway; it wouldn't work for a single-named family site), and .INFO is a true catch-all for every sort of use.