It would be useful to share hardware specs so that we can really recommend something for it. You will get best results by trying out multiple distributions and get a feel. Generally, almost any linux will do, problem will be browser so saving as much ram for it would be useful.
First suggestion: get some used SSD for it if it does not have it already (even 64GB will do), second get more RAM if possible.
Depending on the user I would first go with Linux Mint XFCE, that is lightest easy to use distro I have found.
For someone more advanced/less expectations Crunchbang++ is very light.