Reddit mentions of Visions of a Flying Machine (Smithsonian History of Aviation and Spaceflight Series)

Visions of a Flying Machine, by Peter Jakab
> This acclaimed book on the Wright Brothers takes the reader straight to the heart of their remarkable achievement, focusing on the technology and offering a clear, concise chronicle of precisely what they accomplished and how they did it. This book deals with the process of the invention of the airplane and how the brothers identified and resolved a range of technical puzzles that others had attempted to solve for a century.

I read this many years ago, but it sounds like it's the sort of book you're after. One thing I do remember is that Samuel Langley might have been able to beat them, if not for their experience with bicycles. He had a better engine, etc. But Langley and others were focused on making something that was self-stabilizing. The Wrights realized that a bicycle pushed down a hill on its own would immediately fall over, but an experienced person on top could control it. So they knew they had to learn to become effective pilots before they could make a real airplane. Hence, they started with manned kites. Also goes through their wind tunnel development, and friendship with Octave Chanute.

Not paper airplanes, but metal wing models. The wing models are now owned by the Franklin Institute in Philadelphia. Some are currently on display at the Smithsonian in DC.

Two FANTASTIC books that touch on this are:
Peter Jakab's Visions of a Flying Machine and
John Anderson's History of Aerodynamics

An interesting fact: Dayton was plumbed with natural gas for the street lamps. The Wrights designed and built a natural gas engine to run off this to drive the machinery in the bicycle shop; it was this engine that provided the power for the wind tunnel.