Website question....

I see there are tons of sites out there such as godaddy, that alow you to use there servers..... I Dont Want to do That.

I want to have my own server at home and host my site from it so i dont have to pay monthy fees or yearly fees to use there servers... (I know its alot of work but yea)

my question is that i will be a url. how do i reserve a url so it is MINE... ???

is there a fee? and once i have it is it allways mine? or do i have to pay yearly or soemthing???

thanks

zack