as for the domain no matter what if you want that you will have to pay for it. i get my domains at godaddy.com and they charge 8 or 9 bucks per year for a domain so thats pretty good price. as for hosting you can host from your own home i have done it before and it is easy. once you know your ip address you just set that as your ip in your dns settings in your cp of what ever registar you use to register your domain
if you are goin to use windows to host your site. i recommend using this
http://apache2triad.sourceforge.net/
it is apache, mysql, and php all bundled up into one install and what not and works great when i was playing with it good luck