The Design
Some considerations (a.k.a. "design requirements")
Small "2 seater" factor: Let's build the smallest possible Go Kart that can be comfortably driven by 2 adults or 2 kids.
Off-the-shelf components: I tried to use only widely available low-cost components I could find on Amazon / Home Depot or another big chain.
Electric Motor: The obvious choice for building a Go Kart is to use a small gasoline engine (i.e. 110cc), yet this decision is mostly historical, and usually needed to drive a heavy metal structure. My lovely daughter insisted to use a clean energy electric motor instead and I went with the flow without being disappointed.
Under $700: Well... I tried "Under $500" first - but it required too many compromises, "Under $600" was totally doable, but under $700 made it totally worth it :)
The outcome
Let's try scratching something here (thank you Excalidraw)...
This is more or less "Version 1" design I came up with:

Some of the design decision might seem weird, but they were made based on the component specifications I managed to find:
- Rear axle size is 740mm, just because this is the rear axle of some Chinese 110cc ATV. Front wheels are wider just because this is how steering assembly came (this steering assembly is widely available and dirt cheap) - see TBD.