For starters, you'll need a large group of highly-trained athletes/stunts because even to fake Spiderman's abilities, you need extremely good physical condition.
I mean, even if you have the tech to climb the walls of buildings - which is something achievable - climbing a skyscraper would be an extremely slow and tiring operation which could not be done repeatedly by the same person. I mean your "Spidy" would really be a team. One martial artist in a suit which is preferably made out of ballistic nylon. Reinforced with kevlar on critical points, equipped with a special sort of nolwep to mimic web-throwers used as weapons. (This nolwep would not be capable to provide fast escape/travel, you would need an extraction team which prepares exit roots while the martial artist fights the thugs.) Equiping a team of hidden snipers with such nolweps to provide covering fire is also a presumably good idea.
Climbing walls in a bulletproof suit would not really be an option, your martial artist should hide after a quick leave and a parkour stunt person should do the spectacular leave. This would not really be necessary for anything more than maintaining the illusion. To mimic the travel-by-webshooters effect, you need to apply a few aerialists and a team which preinstalls ropes (because the webshooter technology isn't really available IRL). That makes it... let's say one martial artist, two-three parkour artists, two-three aerialists, at least two snipers and a tech team to install and maintain all necessary equipment. In theory it can be done, but what for?