De Broglie was studying Bohr orbits in 1924. He had a problem and eventually solved it by mathematically simulating a standing wave around the circumference of the line tracing an electron's orbit. In 1925, De Broglie gave the result in his dissertation and it worked perfectly. In 1930 (I think it was 1930...) Bohr was awarded the nobel prize in physics for his explanation of the wave model. The "electron wave" was essentially a representation of the probability density of the electron's position. Shrodinger made a differential equation in 1926 which one could call the beginning of modern quantum mechanics.
I forgot about photons, sorry. Here is the timeline for our theory of light:
1700 - don't know
1800 - don't know, but it's really fast
1801 - Young's double slit expleriment shows a diffraction pattern for light and creates evidence for its wavelike properties
1850 - Foucault measures the speed of light in water
1865 - Maxwell discovers, almost by accident, that light is an electromagnetic wave.
1905 - Einstein describes light as a particle to explain the photoelectric effect
1910 - don't know again.
It is clear that light as a particle came before the electron as a wave. It is important to note that these are mathematical models and we apply models that work. Models which predict nature are possible, but models that reveal nature's secrets are not at this point. Quantum wave models are very good predictors.
In light and in matter we have this so-called "wave-particle duality." A quantum is an individual amount, a discreet bundle. Only discreet bundles of energy are allowed in atomic orbits, so we say that they are quantized. Quantum wave theory is the attempt to describe quanta (like electrons) by waves. What happens when you assume something is a particle and a wave is what has made many of the rules of quantum theory.
I am sorry, but I cannot really name any good websites, but here are some good books, which are out of print but which I was able to find for a decent price on amazon.com:
Modern Physics and Quantum Mechanics - Anderson, 1971
Introduction to Modern Physics - McGervey, 1971
These two are genuine physics texts. They require some real mathematical knowledge on the part of the reader. For an excellent, and less mathematical treatment, try the Feynman lectures or any explanation by Richard Feynman.