Nice looking Spider! "Azzurro Met 876" is the paint color code. In the US, the '83-'85 Spiders are known as the Pininfarina Azzurra.
When Pininfarina took over the Spider in '83, the interior dash configuration, location of the exterior mirrors, and the deletion of the back seat in favor of a true parcel shelf and power windows are about the only significant upgrades. Pininfarina also relocated the windshield washer bottle to be under the cowl rather than up near the radiator. In '85 Pininfarina also reworked the radiator so that the overflow tank is the highest point in the cooling system. Other than that - it's the same as the fuel injected Fiat Spider 2000 series ('80.5 - '82). With that in mind, the availability of parts shouldn't be an issue with the exception of one or two interior parts. I believe that air conditioning was ALWAYS a dealer-added option on these cars. If you have AC on your car, you are pretty much left to your own devices and knowledge of your mechanic or AC specialty shop. It is estimated that having AC on a Spider takes away about 3 to 5 horsepower when it is in operation.
As for performance upgrades, a big brake kit and Computronix ignition system are hands-down the biggest bang for the buck. The Computronix igntion improves reliability exponentially (
no points or vacuum advance or magnetic pick-up to worry about) and the big brakes will have it stopping on a dime. I have both of these upgrades on my '82 and they are well worth it. I wouldn't bother with a lightened flywheel
until you have to replace the clutch or pull the transmission for some reason - but it would be a worth-while upgrade at that time. Everything else is small tweaks here and there. You can opt for some adjustable cam pulleys to dial-in the valve timing. Best to do that if you upgrade the cams. You can also swap out the stock crank and water pump pulleys to aluminum versions to save some weight (same principle as the lightened flywheel). You can also shed some significant weight (and therefore help performance) by removing the big tube bumpers. Adding a rear sway bar will help with cornering, especially if you intend to keep the stock 14" wheels you currently have on the car. Upgrading the shocks is paramount, especially if the car still has its factory-issued set. For high performance go for Koni Yellow. For a good upgrade over stock but less harsh ride than the Konis go for KYB. A set of progressive rate springs will lower the stance of the car an inch or so but still give a nice ride. If you don't have to go through emissions in your area you can get an extra horsepower or two by removing the catalytic converter but be ready for a louder exhaust tone unless you put in a resonator in its place. It is also good to find a way to get outside air to your air box so that it is not ingesting hot air from the engine compartment. All this is well within your $3000 budget, especially if you do some of the work yourself. After that, getting extra oomph from the engine and better handling will get expensive very quickly.
There's a unique enthusiast site just for the Pininfarina Azzurra:
http://www.pininfarinaazzurra.com/. But for maintaining it, resolving issues, and getting help, this site you're on right now - FiatSpider.com - is the best.