(Image taken from MarvelCDB)
I've been playing at least a game a week, and one of the random combinations my generator told me to play was Spider-Man out of the Justice aspect, and I decided to give it a shot.  It's a bit of an odd combo- Spider-Man only has 1 Thwart, which isn't really a good fit for what Justice's goal is... but his other stats are good, and the Justice cards could be used to offset that weakness.  There certainly could be some potential.

My deck:
Justice Spider-Man

Spider-Man

Upgrades
2x Spider-Tracer (Core Set)
2x Web-Shooter (Core Set)
2x Webbed Up (Core Set)
2x Heroic Intuition (Core Set)
1x Followed (Captain America)
1x Endurance (Ms. Marvel)

Events
2x Backflip (Core Set)
2x Enhanced Spider-Sense (Core Set)
3x Swinging Web Kick (Core Set)
3x For Justice! (Core Set)
2x Great Responsibility (Core Set)
1x Concussive Blow (Ms. Marvel)

Supports
1x Aunt May (Core Set)
2x Interrogation Room (Core Set)
3x Surveillance Team (Core Set)
1x Avengers Mansion (Core Set)
1x Helicarrier (Core Set)

Resources
2x The Power of Justice (Core Set)
1x Energy (Core Set)
1x Genius (Core Set)
1x Strength (Core Set)

Allies
1x Black Cat (Core Set)
1x Daredevil (Core Set)
1x Jessica Jones (Core Set)
1x Mockingbird (Core Set)

Okay, so my main plan with this deck is to use all of the Justice cards to help handle the schemes on the board, and still leave Spider-Man free to bust some heads.

There aren't many Allies available at this point, so I included all who I thought were sensible.  Likely, any that come out, I'll use to thwart, except for Black Cat, who will just attack.

Interrogation Room feels like it's a good fit, as Spider-Man has decent offensive abilities, so there could be ample chances to trigger this.  The Surveillance Teams may end up doing a lot of lifting, and combined with For Justice! may end up being the primary means I handle threat on the board.

Followed hasn't impressed me, so I will likely replace it before I play again.

Anyway, so far, I've taken on Risky Business with the Doomsday Chair, and it wasn't exactly easy, but I did manage, and Spider-Man's ability to take on even strong Minions came in handy quite frequently.

Hopefully the upcoming Justice-focused release gives this sort of deck some new toys to play with!