The last go cart I raced was in the early eighties and obviously it wasnt a quarter midget, your milage may vary.
I would go to the local races first and hang out in the pits for a few races several if possible prior to buying anything. I think you will find plenty of friendly people that are willing to share their experiences, and the cost experience. Find out the tire cost, and there lifespan.
I would be calculating the initial start up cost, along with the weekly expenses. Dont forget the simple things like pit passes etc.
I would also find out what are the basic tools you will need.
Does the track have individual weigh scales for each tire etc... that can be used on regular basis by all racers, if not then you will need to consider things like that too. But you can probably hold off on that for awhile, I would just work on making laps initially.
At 10 there is a lot of developmental time. Think long haul if he likes it enough to race for years, you can probably buy big ticket$ items more judiciously after some seasoning.
I would only buy what I must have first.. Safety gear, car and a simple trailer. The pits are probably filled with closed haulers just remember that you cant put those on the track. A lot of folks want to show off there hardware, if you are going to do this for the next 10 years you have to be practical (if such a thing is possible in racing).
I think this is a wonderful Father/Son thing. Plan on at least 10 to 15 shop hours a week. The shop time is good structure and can be as rewarding as the racing. A great technical learning center for Aiden too. I would do the most challenging maintenance and assure all safety components are right , but I would let him do as much he can.
A driver that knows what he needs to make speed has a chance, and that knowledge is subjective. What one driver needs in many cases vary, his knowledge is the best friend he will have on the track.
Best wishes to Aiden.
Last of all I know you are very sharp Matthew, and you will go through the safety issues with a fine tooth comb. I would just make sure any track Aiden competes at has no sharp abutments as in a pit entrance etc. Those things have to many angles that can go wrong.
Be patient, Racing is tough and humbling. There will be lots of adjustments and things to learn. I wish I could be 10 y/o and do this very thing. But again it is very humbling.
Again I wish him the best.