Instructions
Drive to either one of the Perseus stores in Liberty City. One is located in Middle Park East, at the corner of Pyrite Avenue and Bismarck Avenue. The other can be found at the corner of Amethyst Street and Amsterdam Lane in the Exchange neighborhood.
Enter the store and talk to the clerk. You need to purchase a complete suit of clothes, including wingtip shoes. All elements of the outfit must be purchased from the Perseus store and it will cost around $1,500 for the entire outfit.
Remove any headgear, including glasses or masks. Wearing headgear marks the outfit as not being wholly from Perseus, thus the game will ask you to wear "a suit and smart shoes" when you attempt to undertake a mission that requires them.
Drive to Jimmy Pegorino's marker on the map -- a gray J signifies his missions. So long as you have not altered your outfit since purchasing it from Perseus, the mission will begin as normal.