What is the best Linux distribution for old computers?

Arch uses a rolling release model for updates. Unlike, for example Ubuntu where a new version is released every six months, packages are updated when they are ready. The advantage is a very up to date system and that the work of upgrading can be spread over a longer span of time to a point where it is hardly noticeably effort. However it can be difficult for people without a high bandwidth connection, or with limits on how many GB can be downloaded imposed by their internet service providers. A GB a month of downloads is quite possible.

This can be somewhat offset by Arch being lightweight, besides the relatively small core, the user selects what is installed (and has to be updated).