Thats a cool kart! I haven't seen them with two shocks on each wheel before.
If you are wanting to put "extensive" upgrades into it and you have some fabrication skills, here are my humble suggestions in order of what I think is most important:
1. Engine and torque converter, unless you are satisfied with the engine that's on it already. Throw a predator 212 on there, and a 30 series TAV and you're set. You can tweak the predator a million ways, upgrade parts, reject the carb, air filter, etc. But for now, just a stock 212 will be a good place to start, then come back to it after the other mods are finished. And in my experience, those those Chinese made 30 series comet knock off units you can find on E-bay work just as well as the real deal Comet TAV's. Regardless, you definitely want a TAV as opposed to a centrifugal clutch. They aren't that much more expensive and you wont be burning up clutches all the time.
2. Next thing I would look at is the brake set up. I cant see if that has the old band brake set up on it or not. The old band brakes can work decent if adjusted properly, but I am of the opinion that having really good brakes on a kart is essential and it would be worth it to upgrade the brakes to a hydraulic disk brake set up. Especially if you have kids that are going to be riding it. The band brakes work, but they take a lot more muscle to stop quickly than a hydraulic brake set up would take. Ive never been able to get a mechanical disk brake set up to work worth a crap for a kart that heavy. You might be able to somehow rig up a duel disc mechanical brake set up, but it would be a lot more work than its worth and probably would cost just as much as a hydraulic brake set up.
3. Steering. Im assuming that is a live axle set up. Again, other people may disagree with me on this, but I really hated the steering on my old yerf dog. The turn radius on em is awful to begin with, but if the kart is moving slow, or not moving, those things are a nightmare to turn around. And since they don't have reverse, being able to easily make a U turn in them is worth investing in. So I would consider coming up with a rack and pinion steering set up for it. This would probably take a fair amount of fabrication skill and might not be cheap, but again, I think it would definitely be worth it.
4. Good quality shocks. The stock shocks on those things suck. They are fine if its just for kids to run circles around in the yard or ride up and down the street in the neighborhood, but if you plan to take it on any kind of trails, you will want some good quality shocks. I don't have any suggestions as far as what brand of shocks or anything, but consider looking at shocks made for 4 wheelers, ATV's etc.
Those are the upgrades I would be thinking about if it were my kart. Good luck and have fun. Make sure and make a thread to show us what you come up with.