How feasible (I guess in terms of costs) is it to build a real home-made airplane? I guess the obvious place to start is to reproduce the Kitty Hawk plane with modern (ostensibly lighter and cheaper) materials?
If you had $20K it's perfectly possible to build a day only single/twin seat runabout.
http://www.chilton-aircraft.co.uk Plans available free after permission to build from Mrs. Ward.
https://www.pietenpolaircraftcompany.com Plans available for $180. Wood kits with all the wood for specific parts available in the $75-$300 range.
* Assuming mechanical ability and a toolshop and not making the engine.
Wright brothers did it from first principles, built the engine and where bike technicians.
Wouldn't be cheap though for the equipment.
People built planes as a hobby pretty much as soon as they were a thing, the internet and overnight shipping would help, be thousands of hours work though.
https://www.popularmechanics.com/flight/how-to/g631/4-amazin...
This one is really impressive https://generalaviationnews.com/2010/12/05/savor-the-experie...
And he has a site here http://www.aerostruk.com/the-plane/