Re: The classical electron radius is roughly 3 times that of the proton
"This, article suggests that the classical electron radius may not be the correct way of measuring it."
It depends what you mean by "correct". Electrons, like all other fundamental particles, are thought to be point particles with zero physical size. Some theories suggest it might not be exactly zero, but instead something like the Planck length, but certainly far smaller than anything we can even dream of measuring in the foreseeable future. The classical radius of an electron isn't actually a measure of its physical size, but rather a sort of representative parameter that can be useful in some calculations. It gets its name from the fact that it shows up as the non-relativistic (ie. classical) limit of certain equations, such as calculating scattering cross-sections for low energy particles.
The proton, on the other hand, is a composite particle with a real, finite, physical size. The quarks and gluons inside are also thought to be point particles, but since they're separated from each other we can measure how much space the whole ensemble actually takes up. It's a little more complicated since, like atoms, there are the usual quantum probability clouds involved rather than nice little solid balls orbiting each other in a sensible manner, but depending on exactly how you define what it is you want to measure, there is definitely a real size there somewhere.
So it's not that the classical radius is not correct, it's just not measuring the same thing and so can't be sensibly compared. In the size talked about in this article, in the sense of what you'd get if you used a really, really small micrometer to measure them, protons are infinitely bigger than electrons because they actually have non-zero size. In terms of classical radius, the electron is much bigger since it scales with 1/m. However, since that means the classical proton radius is much smaller than its actual physical size, it's not a very useful parameter since other effects will always dominate.