Sounds really cool that you and your son have gotten the bug, and decided to go try some racing. I was really lucky and got to race all through my childhood with my father and I traveling all over doing motocross as a kid. I transitioned into road racing after a few years off of a bike in 2002 on a 750, and the best advice I got was from fellow racers with CCS at that time to get a 600 for the next season. The benefit to the 600 is that you can race 2 solo's on Saturday and 6 sprints on Sunday if you want to........ And nothing will make you get better, sooner than lots of quality track time in a race setting (track days are great, but not the same). The down side to the 600 is that you are in the most competitive classes and at some events those classes can get a bit messy. Just check out the mylaps pages for the winning lap times at the tracks you want to race at, the 600 and 1k times are pretty close from the novice classes through the experts. Most of the people I have met at a racetrack have been very willing to help out and give advise when needed.
There has been some pretty good advise on this post. I will try to add a couple things.
First don't expect to see yourself drop times into front end race times at a trackday, most racers at trackdays will try to be quick, but not risk too much. (Regional Racers will drop anywhere from 3-5 seconds on a race weekend from a trackday pace depending on the track).
Second is to try and find something you can ride in the dirt. It is not the same as getting time on the road coarses but you will learn bike control through sliding in the dirt a bit and you don't need new tires each day, or to travel very far.