You will have to pay a yearly fee for your domain name,
and then use a free service to point to your ip address.
There are tons of registrars out there... don't pay more than $10.
what's your upload speed?
I have a high speed internet too, but my upload is capped at 256k.
I wouldn't want to run my business website on that, hopefully yours is faster.
IMO - It just isn't worth hosting your own site.
I only pay my webhost $20 a month, and I can host unlimited domains.
MySql, php, are included, along with redundant connections to the internet,
tech support, etc.
This is just a small list of reasons why I think you should just let the pros handle it.
Do you have an identical set of hardware standing by in case something dies?
Do you have a RAID setup? A backup tape? UPS?
Just some things to think about.
Hope this helps.