There are a total of 27 equipment upgrades (7 of which are only unlocked upon finding the blueprints). These range from pistol, gadgets, and armor upgrades. Normally you must buy one version and then will unlock others. You can start upgrading with Piero whom is met as part of your main objective in the game. You will have access to him from time to time, mostly inbetween missions. To gain money in the game to actually purchase these, you have to collect money and items in the game by picking them up (looting). You may also pickpocket enemies or loot their bodies. Just make sure you keep an eye out for things you can grab as well. Paintings are worth a lot of money if you are picking them up in your run (see the Art Dealer achievement description for locations). Also, during Mission 5, you will be in a mansion and can loot all of the guests.
Suggestion: You can buy all of the cheapest upgrades to get to your 15 and then reload your game. That way you aren't stuck with things you don't want.