You can have one user act as a server and make sure they open their firewall if it just is a program for a few friends. Due to cheating and so on that won't work if you aim bigger though. If you want to make it more professional I'd suggest placing your own server somewhere (can be your own computer and let people connect to it using your ip, much cheaper than renting a server).
As for applet vs application, why not both?
It's easy enough to convert the one to the other and everyone has their own preference, (Applets ftw!