I have two web servers at home and the are both for hosting pages
that are accessable to users on the internet and me at home. All you
do is get your domain and forward it to your IP. When you access the
domain at home it will just check the domain and forward to your web
server. Your computer would pick up that your web server is local and
access it that way. Then you would not need a intranet server to view
the web site at home.

Acceptable hardware for your web server:

My web server has a celeron 533MHz cpu in it (it is not the cpu speed
you really need) with 256MB of SD-RAM (this is what you need lots of)
20 GB IDE Hard disk, CD-ROM, Floppy, Standard motherboard and a 4MB
AGP Graphics card, no sound or other devices. It has to be plain, the
more devices that are in it the more resources are going to be taken
up.

If you had the server on a faster connection say at 1MB then you
would have a PIII equivilant and at least 512MB to maximise the
performace. The reason my server isn't that fancy is because it's on
a 56K dial up connection.