if youre not experienced with unix-like servers, i would suggest freeBSD. in my experience, openBSD was the hardest to use. netBSD wasnt too much harder than freeBSD, but my experience with it was brief. see what kind of hardware you can get a hold of before you commit yourself to an OS decision... no big deal after all, BSD is free!
im sure youve done the research:
NetBSD: will run on many many many different kinds of hardware
FreeBSD: versatile, awesome server performance, easy installation.
OpenBSD: very secure because there isnt much installed... supposedly the new version is supposed to be very resistant to buffer attacks, it also has a great firewall, pf.
If youre not expecting too much HTTP visits, id say $150 could get you a used PIII (as mentioned), I have PII servers running a few dozen requests a day without any problems (using 128MB of PC100 RAM i bought at Frys for $10), but as Soybomb said, if you run SSH, it could eat up lots of resources.
oh yeah, the knowledgeable forum members reinforced my notions in another thread that a server shouldnt have a GUI, so its probaly not a good idea to install X.