The question about weather or not most ISP's will let you host a server on your home connection gets asked here pretty frequently.
Check with your ISP before doing anything else. Most block port 80 and if they don't they usually do not allow hosting a server on your home connection in their terms of service. I would suggest calling or emailing the customer support at your ISP.
It can be done and there are people who have done it. I wouldn't suggest it, but that's just me. You can get decent colo space for $50 a month and be connected to multiple network providers, have redundant power sources, and greater physical security than most private residences.