Depending on what sort of hosting you are looking to provide, you may have to rethink this quite a lot. If you're just hosting for friends Windows 98/No-IP etc should be fine, but if you actually want to charge for hosting you will need more.
Even if you are not looking to charge, these points may be worth considering:
Windows 98 isn't wonderful for hosting. For hosting the computer must be running at all times, and I doubt you can get Win98 to run for more than a day at the most. Linux (as your friend said) is an excellent choice. Its extremely stable (one development server I'm using has been up for 49 days, I've seens some at 190). Its also highly secure (unlike Win98).
If you do go with Windows (2000 is a good choice for uptime), PHPTriad is excellent to download (its now at:
http://www.sokkit.net/) as it will set up the web server (Apache) and PHP (used for scripting) and provide you with a nice control panel.
If you don't have a static IP I am assuming you are using a cable or DSL line. This could have major implications. Firstly, many ISPs don't allow (or even block) hosting on their services, to stop you doing exactly what you are planning. The second problem is that these have quite limited upload speeds (I'm not sure about the USA but in the UK most 512Kbps cable connections are 128K upload, and most 512K ADSL connections are 256K upload). Its upload speed that matter when hosting, so this should be taken into account.
I haven't used No-IP but it will certainly do what you are looking for. You could offer people domains through 'cloaked forwarding' as offered by many registrars as you will then have a URL for your server.
I think that if you are planning to do this on any sort of decent scale you will need to do a lot more research and look into dedicated hardware and running a dedicated hosting server.
There's also a lot to think of in the way of security (opening up a computer to the outside is very dangerous), support (what happens if someone has a problem at 3am? What if the server goes down while you are on holiday?) and some sort of high-speed connnection with an SLA. It all gets quite complicated at this stage (power outages? backup lines? fire suppression?).
If you really want to get into hosting, a home computer is fine for experimenting but if you really want to make a business out of it try a reseller account or a managed dedicated server and take it from there.
