Yup, it's possible to host it on your own internet connection that you're sharing with other computers. Just tell your firewall/router/linux-box what port you want port 80 (the web server port) to be delivered to, and all will be well. It's actually much more secure that way.

As to your orginal post, you should be explicitly looking for someplace that only allows ssh and not telnet. Telnet is a security risk for all involved, and a competent place will have gotten rid of it years ago.

Matthew