A bit more in depth than above (I'd agree as far as an easy route with the above, but here's the guts of an idea):
Grab a router. Any kind really, heck, even build a linux router box ( www.smoothwall.org
) if you want. Now as you assign IP's to each of your other boxes (or your single box if you bought a router such as Linksys or D-Link) you can choose to have static 'Private' IP's. This helps for things like webhosting (apache) FTP (proftpd) mail (qmail.org) and so on. The problem still exists that you have a dynamic IP though (obviously, or else you wouldn't be wondering how to get a static one
). One of the nice things about the router is that if left on indefinitely (forever) Your IP will tend to remain the same. The need to update your IP with one of the dynamic hosting companies (zoneedit.com dyndns.org no-ip.com) becomes rarer and farther between. You still will have a dynamic IP, it will just change less often.
That's not really broken down too much, so if you have questions on any part (or the entire thing) by all means, ask, I'll be glad to break it down a bit more for you if needed.