Your skills - whatever they are is your best insurance for survival. as for what will be of value; in the city, for the first two or three weeks batteries - in all common and uncommon sizes, lighters and fire-starters. Anything that will give people who live in the light their whole lives a means to see and stay warm at night.
After the first week people are going to be thirsty and hungry. They are going to be dirty and getting sick. If you have water to trade or food it will be worth all the gold and silver they can carry. If you have higene products, soap, or moist facial towelettes the will be worth ammo and small quantities of food or water. Weapons are off limits for me as barter (to give away not the receiving of) but those without will need knives, bows, crossbows, and yes, guns. scraps of stainless steel are good as money to me as is any high grade or tool steel. Pipe and pipe fittings, tubing - copper, steel, tin, and even aluminum all metal tubing has value to me. PVC and ABS tubing is also good but not as good as metal. Lead in large quantities, sheet steel, steel wire, old car springs, empty jugs, barrels and large containers for liquids. All these things can be used to make all kinds of valuable stuff. From these things I can make an Aqua-ponics setup that could help feed a family, a still to keep water drinkable or to make alcohol for drinking or fuel, weapons from arrowheads to knives to guns and even rudementary cartridges for home-made guns that use matches for propellant. You would be surprised the things you can make to repair things that people "need" to feel good or even to survive with a bit of scrap.
Sorry bout the lack of coherrency and punctuation in this post - I am fixing dinner and have to interrupt what I am doing here for the sake of family.