As much as I advocate for people serious about the sport hiring coaches, in this case, you probably won't be able to stick to the most basic program assigned to you. Every program that I paid for took about 15-20 hrs of my week (including travel time, setup/breakdown, etc...). And, believe it or not, most basic to intermediate coaching programs are copy-paste for the coach to assign. It's nothing special. And being that your situation provides less time for training than a normal aspiring elite or master, you'll not be able to follow the 5 or 6 days-a-week program to the letter.
There are no shortcuts. If you are training 2-3 days/week and your competition is able to put in 5-6 days/week, you won't be able to keep up at the big events unless you are uniquely talented.
So, at that point, you will be paying money for a watered-down program that simply amounts to: "Do whatever you can when you can"...which you can manage to assign yourself.
If you want to be a sprinter, know that strength is the foundation for everything. It takes the longest to develop (over several cycles over months and years) and it's the component that takes the longest to decay. So, when training time is limited, that's where I'd spend all of it.
Next is power (which is a function of strength). Then comes endurance (cardio). Then top speed.
Further, you don't need much endurance as a sprinter unless you are trying to go deep in into a sprint tournament, riding keirins, or kilos. But, if you want to ride Man-1 in team sprint for giggles in local/regional events, you can do that off of pure strength lifting with the occasional track session to stay familiar with the curves at speed. That's almost entirely anaerobic.