The thing is, that with an element with leveling up, you want people to get addicted to being successful. Start with a few quick levels and before they know it, they have a few ranks for what they've done. Then it starts to get a little harder, but by this point, they are wanting to get to the next level. I do not see 10 being reasonable, and I would hope people spend more than a few seconds on a picture, especially when they need to make an important decision. I could see a 30 seconds to a minute. Usually the first few levels are regarded as tutorial levels, and perhaps that is what the first level can be is tutorial. Given the short attention span of our current gaming market, if we don't capture their attention fast, they may move on. Getting them excited early is a good way of getting a lot of attention.
Not everyone will appreciate a picture of a kitten, so I don't think that will really work, unless you are speaking of LOLCats, but even then, that won't reach everyone. I don't see what chatroomsor social media would accomplish for something that is meant to be a quick experience. Something we learn in mobile development is that you have to take into consideration that when someone uses an app, they will likely use it for 1 - 3 minutes, unless it is a game, and it can be up to 5 minutes most of the time. Now of course people do play games longer on mobile devices, but not all the time. Given this is a volunteer program, we should assume that people might spend 5 - 10 minutes in this and go back to their game. We'll have to test and see, but having elements that keep them in the plugin longer I think is the wrong direction to go.
Now we could do something where there is a picture with 10 pieces on it and as they get a level, they are able to remove a piece to reveal a special picture. I'm not sure what, but it also helps give them incentive to level up to uncover the other pieces. maybe a special in-game code to get special prizes from the developers or something.