ProZinc is a U40 insulin (that refers to the strength of the insulin - for U40 insulins, there's 40 "units" of insulin per ml; U100 insulins, like Lantus, have 100 "units" per ml). It is possible to use U100 syringes with a U40 insulin, you would just need to convert the dose (see this
conversion chart). The nice thing about using U100 syringes, is that you can give finer doses more reliably and accurately if needed (for instance, with my Rain I was only giving her 0.1 unit of ProZinc at times - a dose that would have been impossible to accurately measure on a U40 syringe unless I used digital calipers). Doing the conversion can seem daunting, especially in the beginning, and you may never need to do such fine doses, so I wouldn't worry about it now. I would suggest getting insulin syringes with half-unit markings if you can though.
I know testing seems very overwhelming, especially when you're still trying to absorb everything else that comes with a new diagnosis. As for "over-kill" with testing before each dose, I usually just think of what I read from one member on here (can't remember who off hand) - if you had a diabetic child, would a pediatrician suggest blindly shooting an insulin dose without checking glucose levels? There's plenty of people who do with their cats (though I suspect most don't end up on this forum), but for me personally it's not something I would do. Blood glucose levels aren't static. Lots of things affect them (appetite, carb content of food, stress, dental disease, other underlying illnesses, etc.). Testing helps ensure that insulin is given in a safe manner.
It's also important to try to get test readings mid-way through the insulin cycle, around the time of peak insulin efficiency to determine the "nadir" or lowest point of the blood glucose (for ProZinc, this is typically around 5-7 hours post insulin shot). This helps show how the insulin is working in your cat's body, and if the blood glucose is going too low, staying high, or showing a nice gentle curve (think of a smile). The weekends are a good time to try to get some mid-cycle readings if work or other commitments prevent it during the week.
Bottom line, take a deep breath and try to relax. You CAN do this. Start with baby steps. It's just a matter of figuring out what works best for you and your cat.