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 and
grml are great, as is
System Rescue CD.
grml 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 and
SliTaz 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 option.
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.
M.