So I have a question to all potentially interested players: if I were to do this, would you prefer a sandbox-style game or a campaign-style game?
A sandbox-style game would be like the group RPs that you're most likely used to, with the emphasis almost completely on character interaction. The GM would be responsible for the initial setting description and approving characters, but the players would essentially build their world themselves. The game would most likely feature the characters staying put in one location, perhaps occasionally venturing out into the "wilds" to scavenge food and supplies.
A campaign-style game would rely much more heavily on the GM. The group would encounter NPCs which could be either friendly or hostile, and have to work together to overcome obstacles. The GM (me) would reserve the right to inflict injury, psychoses, or other afflictions on the characters based on their decisions. Basically, think of this like a tabletop D&D campaign, except that no dice will be used. When a challenge presents itself, the characters would talk it over and decide on the course of action.
Either way, the emphasis would be on plot, with perhaps a little bit of smut sprinkled in. After all, it's hard to have a sexy frame of mind when you're worried about food, water, disease, injury, sleep, hygiene, and zombie attacks on a daily basis. My ultimate goal in running this game would be to see how characters of various backgrounds and temperaments interact under extreme circumstances.
I'd be shooting for a small group of about 5-7 people for the test run (perhaps more if people want to go the sandbox route). Either way, the character template would require you to answer a short questionnaire (e.g. how did you survive the Zombie Apocalypse? What did you do for a living before it all went to shit?) I'm thinking every character would get to pick a couple of Strengths (fast healer, ambidextrous, natural leader, fast learner, huge build) as well as one Vulnerability (asthmatic, hypochondriac, insomniac, weak frame, severely depressed/hopeless, one-handed, etc.) You'd also each get one Major Skill, something that you'd specialize in, that presumably you put into use in your former occupation (marksmanship, unarmed combat, wilderness survival, farming, automobile repair, medicine/surgery, cooking, speechcraft) as well as one or two Minor skills that you've since picked up since the Apocalypse (first aid, knife fighting, musical instruments).