You can use a dyanmic dns service to cover the non-fixed IP thing like this one...
A couple of things to be aware of though...
1) If you're hosting from home, you'll have to configure your router/firewall to allow the traffic in as well. There are security implications with doing this, so if it's a desktop you're running this on and have other files on it, you may be putting this computer at risk. IF this computer connects with others inside your network, they could be at risk as well. Typically web servers go in a "DMZ" with firewalling on both sides (the side facing the internet, and the side facing your internal network).
2) If you're using a typical DSL/Cable connection traffic speeds for download are typically a lot faster than upload. Also, you may have as part of your TOS a clause that you CANNOT host a server. That's common here in the US anyhow.
Hope that helps. If you're just doing this for fun, I'd give it a go. If you're looking to host others' sites as part of a business, I'd be careful of what you're getting into. You could probably get a hosting package and host others' domains as sub-domains of your site a lot easier.