Well, to answer the first question, you probability will need to go out to your local tracks on a race day and ask around. Also bring your kids, that way you can get a sense of their interest level in racing. Once there, usually there is someone who is very willing to lay down the rules and tech qualifications. Then that person or some of the racers there can guide you as to what car kits will work.
I will pitch to you one car idea.
The first is the Team Associated Nitro TC3 Plus RTR or Factory Team Kit version. The RTR version is pre-assembled while the kit version will require building and extra parts that are sold seperately (Engine, Radio, etc). The RTR version's engine isn't ROAR legal but some tracks will let this slide in certain class categories. The kit version of this car will require you to buy an engine and then you can buy something legal from the beginning.
Here is a web link for the car:
If you are working with kids and if the tracks will allow RTR version's engine, I would go with the RTR. Especially if you plan on having more than one car. Building two or three cars is tough and can get expensive.