40 gb old hard drive that is suprisingly healthy (96℅ according to HDDsentinel, more than 1000 days left)
Healthy yes, but if you end up using this daily you'll want to consider swapping in a SATA SSD into it and at least gain some sort of speed.
1.25 gb of terribly slow RAM
Yeah that's low. Is that correct, no corrupt RAM sticks or anything like that to throw the number off?
Do you definitely need Linux with a GUI/desktop environment? I'd expect any flavor of Linux server minus GUI would work fine. Think of it as a little server you spin up and run a few programs maybe for your network or some other hobby.
PS - I think I have a Asus laptop from that era and it had 4GB RAM default, can't tell if yours was just spec'd badly since first purchased.