Hello :)
I don't know if it was me, but normally you should be able to access your IP from the internet, directly, something like this:
http://123.113.134.123/
(this is of course a fake example IP)
You probably already know that... so please don't be annoyed if I repeat it - I'm just trying to be helpful. If your ISP gives you a public IP, but your PC is behind a firewall (that includes router modems, and any kind of "internet sharing") you will have to do some port mapping, that is map a port on your firewall (usually your modem-router) to your PC. If you use "illegal cable internet" or some ISP that only give you a private IP, you will not have this option.
Here is more info about private IP ranges:
http://en.wikipedia.org/wiki/Private_network
You'll need to check out the IP of your PC.
What about hosting? That would probably be the easiest... If you need something special I have a VPS and can install whatever software is needed on that and give you FTP access for testing, if you want.
There is also something else you could do, it is also possible to tunnel traffic from your PC to a public host. But that's the most demanding solution.
Hope that was helpful.