Hi, and thanks!
Hmm, I have no experience with Hamachi, but I would recommend downloading Skulltag and then getting the proper WADs. You can make a .zip with all the stuff you want to play, that's fine, as long as the people on the other end unzip it. (trust me, I've dealt with people who don't unzip the .zip files...><)
As for playing together, you could always use Doomseeker (included with Skulltag) to create your own password-protected server and play on that. That's pretty simple as well.
Good luck!
