I am surprised at finding precious little information on how to select
wheels and tyres when designing a plane from scratch.

At least, what are the criteria?

max gross weight must surely come into play.

type of runway? there are tundra wheels, but I find no difference
between concrete/asphalt vs. grass runways?

taildragger/tricycle seems to make not much difference either, many
planes available in either config, with no change of main wheels? which
makes me understand why my instructors insist on delicacy with the nose
wheel.