Electricity and magnetism are both aspects of the same thing (electromagnetism), and are both communicated by photons. To get some sense of how they are the same thing, consider a stationary charge, which produces an electric field but no magnetic field (since it is not moving). Now someone rides by on a train. From his perspective your charge is moving, and he will measure a magnetic field as a result. The equations of electromagnetism make it work out so that even though you and the person on the train think that there are different fields present, you both predict the same motions and forces, so both of your perspectives are equally valid.
The photon is the electric force boson, and when I heard this I was first confused. Then it made sense- that is why lightning is so bright.
No--lightning is bright because it heats up and excites the air molecules it passes through, which then emit light. The brightness does not come inherently from lightning's electrical nature.
there aren't insulators for magnetism like there are for electricity
What would an "insulator for magnetism" be? There are a few concepts here: there is a thing called electric current, which is the flow of electric charge. Insulators are materials through which it is hard to pass an electric current. There's no such thing as magnetic charge (though people would be
http://en.wikipedia.org/wiki/Magnetic_monopole" to find some). Hence there's no such thing as magnetic current, and no such thing as an "insulator for magnetism" in the most obvious way of interpreting that phrase. Electric charges produce both electric and magnetic fields, and both of these can be blocked or excluded from a volume by certain materials, which is possibly what you meant?
So how does "spin" fit into this when the charge isn't even moving?
Spin refers to the fact that elementary particles have "intrinsic angular momentum." A spinning classical ball also has angular momentum, but quantum mechanical spin has important differences. For one thing, you can calculate in classical electromagnetism that a spinning charged sphere should set up a magnetic field. Charged elementary particles with spin (such as electrons) do set up magnetic fields, but their strength is different than the value predicted classical. The explanation and accurate calculation of this fact is one of the triumphs of quantum electrodynamics.
Gravity is the only force that there doesn't seem to be a boson
People like to talk about gravitons, which would be the carrier bosons of the gravitational force. But a good quantum mechanical theory of gravity hasn't been worked out yet, though everyone assumes that such a theory exists.
Vanadium 50 is right in that the depth of your understanding in these topics will be directly proportional to how much math you work through from textbooks.