l really agree with your opinion about itch.io been flood filled with horror games, l also don't like that. It ruins all the other beautiful games that are hidden on this site.
About that first game, this question isn't that easy to elaborate because it's everyone personal opinion, but that first game wouldn't even be an itch.io game, it would be Tomb Raider :) They say start with baby steps and in reality l agree with that. Anything on the internet, even this "platform" might become dangerous for younger existences as they don't know how to protect themselves and might result into the exact opposite you wanted to happen. So imo the best way to handle the situation is by NOT allowing the children to reach the internet by themselves. (Kinda got out of the theme but l think l do make some point).