As a collector of old hardware, I think I have a sense of where the OP is coming from: some hardware isn't worth even an additional $10 investment. The interesting challenge becomes one of finding the best use for the thing rather than "bringing it up to date".
@OP
I have run Lubuntu on 256 MB of system RAM. You won't be able to run more than one or two apps at a time, but sometimes, this is all you need. Browsers, however, are memory hogs, and, in its default configuration, the system will quickly go to swap, which has the effect of making the system feel extremely sluggish. You can remedy this to a large extent by setting swappiness to a low number like 10. Instructions are
here. However, if your video chip has no dedicated video memory of its own, then your laptop is designed so that it must share the already limited amount of system RAM it has with the video subsystem. This is why many members recommend beefing up your RAM. If this were your production machine, such would be my recommendation as well. However it is clear that you are intending this machine as a solution looking for a problem, so here is my suggestion:
Get your little son a better machine capable of running a proper OS and that is capable of growing with him. Use this ancient thing instead as a command-line-only server/gateway. Some uses include: file server, print server, install rsync to make it a redundant NAS, torrent server, media/music server, vpn-capable router/firewall, or just use it as a spare machine you can monkey with and learn the command line on.
To install a basic command line OS, @fantab's recommendation of the alternate installer is just as valid as for a minimal GUI.
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