Okay I'm going to put up a warning right now this guide will contain possible spoilers, you have been warned.
Alright there is 13 costumes in total, 3 of which you have from the beginning of the game which are The Vigilante suit, The Amazing Spider-man suit, and The Amazing Spider-man 2 suit.
Now a majority of the other suits are unlocked by completing 'Russian Hideouts' which will appear every chapter the suits gain through this are the Ultimate Comics Spider-man suit, Big Time suit, Scarlet Spider (Kaine) suit, Spider-man 2099 suit, Flipside suit, and the Spider-Armor suit.
Okay now onto the spoiler suits, again if you don't want to possible spoil the game stop reading now and move onto the next paragraph. Now you unlock the Ricochet suit by beating Black-Cat in the museum and then you get the Spider-Carnage suit by beating Carnage at the end of the game.
Now for the home stretch two more suits. Alright you unlock the Hornet suit by completing all 15 races throughout the city. Now for the one that gave me the most trouble obtaining The Superior Spider-man suit, you unlock this suit by completing all 12 combat challenges located at the Comic Stand. For this I would recommend waiting until you've completed all of the 'Russian Hideouts' as I had to switch suit bonuses a few times to complete the challenges.
Woo! We're done! Hopefully thanks to my guide you now have all the suits unlocked. See you again True Believers!