That website is exactly the type of thing you are looking for, although it will cost you monthly. If you have a good computer with adequate cooling, a fast connection and can have your computer on at all the times that your friends will want to go on the server then you could host your own for free. Go to http://www.speedtest.net/...edtest.net and record your results. Then check http://canihostaminecraftserver.com/ and see how many players your server can hold from doing this.
If you chose to host your own then you will have quick and easy access to all of your server files and be able to make backups easily. Here are some websites that will assist you in creating your own server:
http://bukkit.org/
http://wiki.bukkit.org/Setting_up_a_server
(If you use bukkit rather than the vanilla server software then your server will run more smoothly and you will be able to install permissions plugins and other useful tools like worldedit)
Here are some links to useful plugins that I have used in the past:
http://dev.bukkit.org/...ssentials/
http://dev.bukkit.org/...worldedit/
http://dev.bukkit.org/...orldguard/
http://dev.bukkit.org/...reprotect/
http://dev.bukkit.org/...issionsex/
Hope you get your server up and running soon!