A home webserver is a webserver hosted off of a cable modem, DSL, and in some rare cases a T1 from home. A dedicated/co-located server is a server hosted by a company like
www.colostore.com or
www.layeredtech.com ect.
I don't know who your ISP provider is, but in order to run your own DNS server you need a static IP from your ISP provider. Some ISP providers provide this service for a small fee.
You could run your own DNS server off of 1 IP. And use
www.zoneedit.com as your secondary DNS server. They do offer a secondary DNS service. But the first thing you need to do is get a static IP.
I am not trying to discourage you, and I do not know how many websites you plan to host. But it would take you less than 5 minutes to set up Zone Edit. They even offer a dynamic DNS update service, you can run a program to update your IP every time it changes. And you will not have to pay for a static IP address. Unless you can buy two static IP addresses off of your ISP provider you still are going to have to use a secondary DNS service. I would say 99.9% of the home webservers do not run their own DNS service.