Well, as someone who works in the industry I will say, do not wast your money!
First and foremost, you do not have the correct connection to a network to run a server (web server) from your house. You need a large bandwidth pipe connection in order to do this, and your ISP (home internet service provider) will not allow you to even come close to taking up the required bandwidth connection required to connect to their network.
The type of servers you can run from home, as partially explained, are only media share stations, backup stations and low level file sharing. Meaning you could run a very small low traffic website from your house. Lyte could not run this forum from her house. The bandwidth would get used up in a week (give or take) and her ISP would shut her service off. (I know everyone thinks your high speed connection is unlimited, but its not, you can find many articles regarding this on google, and you can test your ISP yourself if you wish, they get pushy and some like comcast will turn your service off and not let you back on if you use too much bandwidth in one month.)
If you really want to own the server you site is on, you need to look into collocation. You can purchase a web server (a good one) for around a grand (duel xeon 2.8, 2gigs ram, 2x250GB drives, proper network cards, proper server casing, ect.) and then pay anywhere from $80-$200 to have it in a real datacenter, with proper connections, and of course, the bandwidth.
Collocation, means you are paying to rent the rack space in the center and the bandwidth, but that is all, this means if a memory stick or your drive goes bad, you have to buy one, ship it to them, and pay them an admin hour to replace it for you. Its about the price of a good quality VPS or reseller account [well, from the right company, you get what you pay for

].
A good colo center, is located
here, they are located in Portland OR and area very decent center. We currently have 14 servers located in this center ourselves. We also have many in other centers, including LiquidWeb, G3Tech, and a few others, but those are more on the expensive side of it, ranging on the $200+ side.
But back to the original idea, running a web server from home. If you wanted to run your site from home, and it is a small, low traffic level site, and you do not plan on selling hosting, then you can use your own computer, if you are running linux. Any Red Hat distro (fedora, enterprise, centos, ect.) would be best, you do not want to use Ubuntu or any of the GUI distros.
I know many people who do this themselves actually, for family type websites and what not. And the best part is,
you don't even need a server, just a regular cheap old PC. All you really need is an old PC with 128mb of ram, a 10gig hdd, a router, and a linux distro installed.
And if your a really brave soul, you can run it on your own computer (your main one) running windows using IIS, but this opens up such a huge security risk, and your putting all of your HDD out on the net, and your little firewall will not be enough to stop a real hacker from gaining access to your whole desktop. If you want to take that route,
read this, and continue at your own risk! You should also
read this.
If you want to try the linux way, the safer, smarter way

,
read this.
And I will leave you with the usual, google is your friend!
So in conclusion:
You can not run an actual web server from your house, you will not have the proper network connections, as you can not connect a real server to your modem. You will need to contact your ISP to see if you can even host a home site on an old pc, as they may not like you taking up so much bandwidth. If they will allow it, go bargain shopping or pull that old dinosaur out of the closet and download linux distro with auto installing
L.A.M.P., and but a cheap router, and get reading! Or if you really want to own a real web server, go collocated!