Quetion

as an aside what's the most basic functional 'car' you could build

You're right. Their motorcycles start from 30k and the engine is obviously gonna be expensive. That's a nice reason.

theoldmotor.com/?tag=cyclecar

You have to figure out how you want to do your final drive and suspension. It may be easier to use a FWD engine and trans instead of a bike engine. That way you can use modified CV driveshafts from the car you pull the engine from.

just buy new kawasaki zx125s and take it's engine off and put it in your car and use it's parts to make your own car from it. I mean multiple zx125. Don't say I'm stupid, OP already said he accepts any ideas.
Also i heard they are pretty peppy too.

they can be made of wool lol

Surprisingly easy if you're willing to use components from other cars. The more bits you design yourself, the harder and more expensive it becomes.
This is why small-run sports cars are so expensive.

But with some aluminium tubing, a superbike engine, and a few wrecked cars to scavenge parts from, not so hard.
Of course, I like the idea of grafting the front of a small but well-handling hatchback onto a basic chassis, and swapping a bike engine in for more power.
It'd be FWD and slow around the track, but I bet it'd be fun to throw around.

The difficult part in a project like this isn't building the frame or getting the parts, it's making everything to work together.

That said, you will need to know about/how to do the following, among other things that I'm sure to forget:

Load calculations (wouldn't want it to snap in half on the first bump)
Proper selection of material based on the above (since it's a track car you'll want to balance weight and durability)
Complete wiring of the electrics; this will either be really hard or really easy depending on how much stuff you pull straight from a production vehicle*
Plumbing for braking, cooling and fuel (along with possible upgrades to systems)
Build and fine-tune suspension; choose appropriate shocks and springrates for final vehicle weight

If you want something like your pic you'll also need to learn how to build the fairings for it, aka work with plastics.

If you're going with a motorcycle engine you may need to redesign the lubrication system as the ones found on motorcycles typically aren't built to deal with lateral G's (aka oil sloshing to the side of the oil pan in a long turn, starving the engine of oil -> bad times ensue)

*Most serious projects I see just completely rebuild the entire wiring harness, this allows them to shed a lot of weight and complexity by getting rid of the 9 quadrillion sensors that a normal car has (airbag sensors, ambient temperature sensors, shit like that). They usually install an aftermarket ECU when they rewire the car.

here again.
As says, it can be really easy or really hard. If you just want to take a FWD engine and mount it in the back of a chassis/frame you built it can be fairly simple.

If you want to use a motorcycle engine that, as far as I can tell, doesn't come with any ECU, fuel system or final drive it's going to be a lot of work. Not impossible, of course, but a lot of work.

I'm not trying to deter you, I love projects like this and had plans to do one myself a while back but I just realized I didn't have the time at this stage in my life so I've postponed it.

I dont know what this book is like, but i have the guys one on a homemade buggy and it's pretty good. Might be a good start. Dont expect it to be that cheap though.
Why not just buy a race car instead?

Google Locost

Was also going to recommend a Lo-Cost. If I didn't have my eyes on an 818 in the future I'd love to build one of those.