You can use a free hosting service too, or, as stated by Ashley, get some cheap ones (there's some costing 1$/mo).
Of course you have to remember that you always get what you've paid for.
I suggest you to check webhostingtalk.com or hosthideout.com to find some hosting offers/reviews. They are really good boards.
This "Opera Unite's Server App" seems like a standard webserver, like Apache and IIS. If you want to host in your home, forget about this and get Apache, create a no-ip.org account, bound the domain to your IPaddress and voi-la! =P