Yes, you can use XP Home with XP Pro on your home network. Remember though, Microsoft only allows the operating system disk to be loaded on one computer regardless of whether it's an upgrade install or a clean install.
I have a second computer in my home which I want to upgrade from Windows Me to Windows XP. I have found Windows XP Professional discs (OEM) from reputable online merchants at a cheaper price than XP Home. I don't know how it can be cheaper. Can I network the two computers with one using XP Home and the other using XP Professional? If I should purchase XP Professional, can I install it also on the computer using XP Home to upgrade it to Professional without any problems?