You can get Apache for free (see http://www.apache.org/licenses/ for the licenses, but basically, its free for regular use) from http://httpd.apache.org/ . For the smallest, older version, you'd need about 13MB to install. After that, it'll take up about 3MBs, or at least so the manual says. I'm not sure about the CPU speed required, but I had it running (swiftly) on a PII once - so I guess it'll run on just about anything that isn't exceptionally ancient.
Notice that Apaches power lies in its modular design. That 3MB will get you a small webserver, perfectly able to serve html, but not much more. Additional modules will take up its share of system resources, but still, using anything above a 600MHz machine will get you good results for a website like yours. Don't worry to much about it, unless you plan to run a webserver from something really, really, really old. Maybe in those cases Apache wouldn't be your first choice, I'm not sure.
As a last note: make sure to reserve some disk space for your webpages too. Media (images, flash, movies) can quickly take up space. Its all in de design of your website, and the content you want to provide.
I'd suggest you start at http://httpd.apache.org/ and take it from there. Take your time, read the manuals, and start tinkering. It can be quite fun, getting stuff to work. Maybe you'll end up running your own forum or photo album (again, free applications available) after a while!
If you're really into java, its not hard to implement applets in your pages. Going deeper into the web/java combination, this page might interest you as well: http://jakarta.apache.org/site/java_at_apache.html
