I hope you don't mind a couple of comments regarding your nice description?

Accelerating with respect to what? I don’t believe that this is a valid definition of an inertial frame of reference. It makes one question what one is accelerating or not accelerating with respect to. For example: Consider a frame of reference in free-fall in the Earth’s gravitational field (or better yet, a uniform gravitational field). Such a frame is considered to be an inertial frame of reference. Most people would say that this frame of reference is accelerating. It’s accelerating with respect to the Earth.

An inertial frame of reference is defined as a frame of reference in which the law of inertia holds good. That is to say frames in which F = ma (really dp/dt)

Basically what this means is that a frame of reference in which Newton’s first law, a.k.a. the law of inertia, is satisfied.

If you used this definition then when the reader goes on to learn general relativity he'll be prepared, i.e. he won't have to unlearn anything. This is true since free-fall frames are considered to be inertial frames of reference in GR. And in GR a free-fall frame is accelerating with respect to the earth's surface.

I disagree. An observer is commonly definition as just another term for “frame of reference.” You can find this definition in such textbooks as “Introducing Einstein’s Relativity” by Ray D’Inverno as well as “Exploring Black Holes” by Taylor and Wheeler. Eg from “Exploring Black Holes” Glossary, page GL-5

Observer – Collection of rods and recording clocks associated with a given frame of reference.

Thus when an observer accelerates his system of clocks and rods, which is attached to him, accelerates with him.

Personal Opinion - The second postulate should read “ The speed of light has the same value in all inertial frames of reference.” Or you could say that the speed of light is invariant, but that’s mathematical. I’d go with this one here since “constant” might be confusing for some layman.

Note that accelerating observers measure different speeds of light.