Ok. Finally a thread I can speak into.
First things first, where do you live? There are a few club tracks around Texas, but they are all far apart. Our home track is Waco H.O.T. Kartway. I HIGHLY reccommend this place if you are just starting out because it is very family freindly and helpful.
The LO206 classes is where you'll want to start. It's the easiest and cheapest and they still feel like you are going 100mph. Someone else mentioned Chonda. That's not a thing anymore at any of the tracks around here. LO206 basically is the same thing, but using a spec Briggs and Stratton engine. Chonda (Clone-Honda) used the predator engines from harbor freight. They were too inconsistent to be considered a "spec" class.
An LO206 motor brand new in the box is around 700. With the exhaust and few other parts you'll need to actually go racing you are looking at 900-1000 depending on which clutch you get. Don't worry. The clutches on this level pretty much just work. Buy one and install it. Ask the guys at the track you are looking at what gearing you should buy. Then buy a few teeth up and down to be able to adjust your gearing at the track. Use the split (two piece) sprockets.
You'll want to buy a "Jr" or "Cadet" chassis for an 11 year old unless he's really small. That will last him for a few years most likely. At least enough time to figure out if he wants to continue or quit. If he get's good he can move up to the Senior class at 15 iirc. That's when you would want a full size chassis if he's big enough for it. You can keep using a cadet chassis in Senior LO206, but you'll change the rear wheels out for the larger size and you'll have to weigh 360 pounds kart and driver. Some little kids in kadet karts have trouble making weight without using a bigger chassis.
The number one thing I would suggest is just go to the track. Buy a pit pass. Talk to folks. There's a chance they'll let him drive a kart after the race. That will of course get him hooked so be prepared.
If you do get in to it. Be careful of being a little league dad. It happens pretty easy, and I've been guilty of it myself. You watch from the sidelines and just wonder why he's going so slow, braking too early, not on the race line, etc. It's all new to them. They have no experience. Not only that, but I would suggest you get into a kart yourself and see just how incredibly fast the world starts flying at you while you are 1 inch off the ground. It's a lot tougher than it looks. It's also very physically demanding. Get into a kart youself before trying to offer any advice or criticism.
If you guys want to try it out, I can not tell you how good of a place the Waco track is. Years ago when we started it was a bit rougher, people cheating, too much drinking, etc. Today, none of that exists. It is a super family freindly place. Lots of kids, and the other classes are growing. In fact they are going to run a vintage class this year and I'm thinking about getting myself a vintage kart just for that!
This is my Son #96. He started when he was 6 and is 19 now. We've had to take this last season off because he started at A&M and the homework is kicking his butt! lol