I don't know if it's been suggested already because I'm only about half-way through this thread, but this is for those suggesting fully customizable characters:
I personally don't want a customizable character. I love the story that TTG tells, and trying to combine wonderful storytelling with a player's customizable character is not only hard, but unnecessary.
If TTG has a clear-cut end, I would suggest this -
Make a sandbox finale. If TTG plans to make only 5, 5-episode seasons, after the last episode of the last season, put out a FO3-esque sandbox "finale".
I mention Fallout 3 specifically because it had a wonderful blend of powerful storytelling, plentiful quests, the option to complete the main quest right away or not, a giant world, and complete and utter wonderful sandbox-ness. lol
When TTG is done with its version of TWD, I would love to see their version of a sandbox TWD game.
Edit -
I think that a woman protagonist would be the most fun for season two. Not necessarily any woman we've met before, in fact, I would hope not.
There was a novel I started to read once (wish I could remember the name) where an abused wife narrowly escapes being eaten by her two children and husband only to become a very strong and capable leading member in a big group later on.
What I loved about Lee was that I always had that butthole-pucker moment when he met someone new. Would his being black effect how they treated him? Were they racist? And he did get the 'boy' comment more than once through my game play.
I know as a woman, if I was in a small group and we ran into a big group with a lot of guys, I'd be worried about being raped, treated like currency, being a second class citizen. At the same time, there may be groups that would idolize women because stereotypically we wouldn't be very common.
I know that right now, I don't get my hand shaken, or I get that gross hand-touch thing. I still have men try to exclude me from conversations, and sometimes I get the distinct feeling that if other people weren't around, I might be in trouble. (Of course, I only feel this way when I realize someone it actually stupid enough to think I couldn't defend myself

lol!)
I would love to see the same adversity Lee faced brought to a woman.
What I think would be very interesting would be playing a moderately attractive 30ish woman (somewhere around Carely's looks, I guess), who is on her own until she meets a teenaged boy. I know it sounds funny, but I'm talking late teens (16-18). This woman would be old enough to have a 15 year old. That could even be part of her back story is that she made dumb choices, was a teen mom, worked her way back up, and then this shit happens.
Maybe she had an abusive husband and stayed with him because he took care of her and her kid even though he was mean.
So now she has the choice to form a group with this young boy who obviously finds her attractive and risk sleeping next to a guy who may or may not be all that good, or to go out on her own.
I also think the dynamic would be very interesting. He's strong enough to maybe overpower a woman, but not so strong that he could protect a group. The main character would have to be the "leader" (just as Lee really was the leader). At first he would really be more someone to be skeptical of, protect, and trade sleeping shifts with, but watching the two grow and form a larger group would be interesting, too.
Please keep in mind I'm not talking another Ben. I'm talking about a stronger, smarter teen than Ben, maybe one who had a more questionable background than "band geek". Maybe stoner/slacker, or school-skipper. That stereotypical AEP kid that only really ever went to automotive class. (Another neat attribute among a group - having a mechanic/machinist.)
I hope that isn't too rambling, I just wanted to get it out in the shortest way possible. (Possibly leaving things out along the way lol.)
Edit again -
I also think it would be fun/funny to have the new group stay the night in Clem's tree house or some other kind of fun little shout out to the previous characters. :P
Another edit -
Playing as a young child (5-12 years old) would be interesting. As would playing a 13-15-year-old. As a young child, you would have to rely on people, have the choice to be more like Clem, be completely useless, or maybe even be too hard. (Darker than comic-book-Carl, where you are capable like him, but have none of the humanity).
Playing as a young teen would also be interesting, especially as a boy, because you get that awkward you are no longer a kid, you are old enough to take care of yourself, but because the adults around you are used to you just being some young high schooler, your opinions and wants are undermined.
Anyway, I'll try to shut up with the suggestions, my post is getting a bit long lol.