Is it me who have a poor understanding, or does all matter have to become 'pure energy' in order to achieve speed-of-light speed?
If so, does that mean that no material can achieve the speed of light and remain in its original state of matter?
Your understanding is spot on, as is PhotonicBoom's Answer. Something that might give you a bit more insight along the lines that you are thinking is if I answer your question backwards: the property we call "mass" (or "rest mass") is acquired by a particle with a rest mass of nought when that particle is confined in some way. If you look at my thought experiment here you can understand that if you put light into a perfectly reflecting box, the box's inertia increases by $E/c^2$, where $E$ is the energy content. This is the mechanism for most of your body's mass: massless gluons are confined by being coupled to, and by coupling, quarks in the nucleusses of your body's atoms and are accelerating backwards and forwards all the time, so they have inertia just as the confined light in a box did. Indeed this is how most rest mass in the World arises; the Higgs mechanism itself (as I understand it - this is outside my field) is an interaction between otherwise massless particles with the Higgs field. "Coupling", aside from being cross coupling terms in Schrödinger and other quantum state evolution equations, is physically a kind of tethering of particles: they are no longer free to run off at the speed of light but are held back by each other. Even the fundamental particle the electron can be thought of in this way, if you look at my other answer.
Any body as you say with rest mass cannot fully reach the speed of light, as you would need to supply an infinite amount of energy to accelerate it to that exact speed. We do know thought that all massless particles do travel at the speed of light. Are they pure energy? They are, but then, everything is as we know from Einstein's relation $E = mc^2$. I assume by matter you mean solids, liquids and gases, and in that sense you are right, as I said above nothing with rest mass can achieve the speed of light. They can go infinitely close to it, but never fully at $c$.