Since this is based on the game, the preference is to play the characters that are already in the mobile game similar to how they appear there. However, this only applies to characters that have appeared prior to and including the Spiderman Special Event. Any characters that appear after the fact (and Hawkeye, since he's only appeared once briefly) do not fall under this, and you do not need to update the character to match unless you want to.

Ultimately, this is just a preference. How you wish to AU the character is your choice, regardless of if they've been in the mobile game or not, as long as they are recognizable as the character via their personality.