Wow, that looks too good to be running on dirt! LOL!
Judging by the radiator and four wheel brakes I'm going to guess that was originally set up as a shifter kart (125cc MX 2 stroke with transmission attached). You didn't mention what you're going to power it with, but if it's a backyard track I'm going to guess a Chinese 4 cycle of some kind? Shifter kart chassis are pretty stiff to handle the horsepower of the 125, and you'll need to free yours up to make it work.
We've run a few races with our sprint chassis on a dirt oval. I'm certainly no authority on what you're trying to do but I think some of the things we've learned will apply. Loosen the bolts holding the inner right bearing carrier on the rear axle so it can float in the mount, or if you happen to take the axle out, take that bearing off and leave it off. The length of the rear wheel hubs affects the stiffness of the axle - longer hubs = more stiffness - and yours has some really long hubs. That looks like a 40mm axle in your kart, they're pretty common in that era European karts. Measure it to be sure. I'd check on ebay for someone selling a selection of used 40mm hubs of different lengths. Start with the shortest one. If your kart seems loose in the rear switch to a longer one. Also, sliding the rear wheels out takes away grip, in gives you more grip. We use this adjustment all the time to adjust to changing track conditions. This is a pretty sensitive adjustment, just 1/4" in or out will make a noticeable difference. Front wheel spacing is the opposite of the rear wheels - moving them out gives more grip, in takes grip away. This is also a sensitive adjustment, 1/8" either way will make a difference. There should be a bunch of wheel spacers on your spindles to set the spacing where you want it. As for a starting point for your setup, I have no idea! If you can figure out the exact model of your CRG chassis you can probably find a starting setup for it on line. It will be for sprint racing, but we've found that our pavement setup wasn't very off to run on dirt. If you can't find that info, I'd start with 50/50 side to side weight balance and 42% of total weight on the front. Set the front wheels at 1/16" toe out, and have someone else measure it while you're sitting in the kart because your body weight flexing the chassis will make it change. Set the wheel spacing about mid-way both front and rear and see how it works, then adjust accordingly. For tires, we found that Vega Whites work pretty good - 7.10 x 5 on the rear and 4.50 x 5 on the front, with tire pressures in the 3 to 5 psi range. They're already a soft compound, but a generous application of Goat P makes them even softer if you want to mess with that stuff.
My apologies for the VERY LONG post! I'm retired and have all kinds of time in the morning while I drink my coffee, so this happens from time to time!