Hi Matt,
please put some structure in your text.. paragraphs line breaksetc.
A wall of text is a huuge PITA on on phone screens.
Now that aside (and only because there IS punctuation and you're not the laziest guy this week

)
300 is a tough goal, hardly possible with all new parts...
let's see:
a my1020 PMDC motor (1000W) can be had for less than 100 bucks,
it's matching controller for roughly 30 (sometimes 50...)
[the cheapest kart worthy motor I know of atm]
half of the budget gone, nothing achieved so far.
You'll need batteries -at least four- cheapest are lead acid..
picking small ones and that will add up to 200 bucks (50 a pop is reasonable)
See we already cracked the limit and have NOTHING but the powermodule yet.
PWM throttle ~20 bucks, some wires, chain sprocket another 50 perhaps
and we still have no kart to mount it to no wheels, no steering no axle to drive.
You need a frame; and NO wood is not a good idea, it never was and never will be, especially not for a beginner.
Simple reason is this: to make a sturdy and worthy chassis
you will need to put eight times the labour
and about three times the money in making a chassis,
than you would need to making it from steel.
welds are more reliable and cheaper than bolts
and you don't need to tinker with wood grain direction,
lamination for structural integrity and stuff alike.
So no, simply don't!
get the free plans from KartFab.com and take a very close look at those.
Those are good, and free, the resulting kart is sturdy and relatively cheap to make;
OR which I highly recommend, check the local classifieds for a cheap rolling chassis..
in most areas you can find one for relatively cheap, relatively complete..
no way to make a kart chassis cheaper ..
much less find parts cheaper than already mounted to a kart
(wheels, steering, axle, brakes etc..)
Since you need to make eight karts..
maybe you can get a discount for the motors and controllers (with PWM pedal throttle)
at alibaba.com
(min orders usually start at ten, still reasonable to have two more sets and still pay less total

)
oh look:
https://www.alibaba.com/product-det...l?spm=a2700.7724838.2017115.20.7167631eFEVkj5
But even if, you'll need about'ish $100 per set and with batteries the 300 are already gone..
(since that offer doesn't include controller, pedal and stuff)
And shipping will take a while

really I can't see how that's going to work
'sid