The box isn't fit for use with Ubuntu
- too little RAM (128MB is too little for Ubuntu
- the site actually says so!), and probably some hardware recognition issues, but not necessarily bad ones (PIII normally sits on a solid platform that's well supported). You could use use a console based distro to determine what's up hardware-wise; Finnix
are great, as is System Rescue CD
also can run a minimalistic graphical session. But they're specialised distros.
You'll generally be better off with a distribution optimised for old computers; there are quite a few of those. If you want to use it for web only, you can use a minimalised window manager without a lot of drawbacks; Puppy Linux
feature such a setup, as does Tiny Core Linux
(but you'll have to customise that before you can use it for the web - which is its strong point, but maybe not for newbies). And you can also use Debris Linux
with the Openbox
You may also get lucky with CrunchBang Linux
- I've got mixed results, but it's also based on Openbox
and will give you a full-featured distro if it works for you.