I was thinking about this again today. Some things I'd like to focus on are the joys of physical objects, the joy of receiving things in the mail, and the joy of... anticipation. I, personally, like typing more than I like writing but I do like writing -- the feel of pen or pencil or whatever scratching (or sliding) on paper. I've been thinking about mail-in forms as the primary mode of interaction. I don't know if others get as much enjoyment out of those as I do.
... uh, now, before you call me weird, I need to be clear. Mail-in forms suck because they're always for sucky and boring things. But for interacting with a game, I think that filling out a form with your intentions, with your guesses, would actually be really fun! Consider filling out character sheets, or ticking off boxes in Clue if you ever did that.
And everything that you receive in the mail should be a wonderful physical artifact so that if you're at all inclined to treasure flat paper or card objects, you will be able to treasure it. I can slack a bit on the mail-in form because otherwise you'll be sad to send it right back to me, but every other monthly thing you receive should be a small piece of art, something that feels tangible and solid and keepable.
edit :: It's not something I mentioned at first but, naturally, I want to bury depth in the game. I do it out of habit and responsibility and personal need. Keeping the reports, even a copy of your mail-in form... these things should and will allow you a glimpse at some deeper systems. But I think being able to enjoy the game month-to-month without needing to worry about how many of these deeper systems you understand is actually ideal.