Ah. I found the answer to my question about the transponder key, and I thought I'd share it.
Basically, because the engine-management computer will refuse to boot unless it detects the key - you must have a key for it to sense. You can't just bypass it, as the computer controls the fuel injection and ignition (both rather important components of the engine).
What is done, is to disconnect the antenna connection to the ignition switch and to connect it to a wire wrapped around a key. This key is then concealed under the dash. This allows the computer to detect a key and boot when powered-up by the remote starter. For security, once the installation is completed, the key is cut, leaving only the transponder-containing fob.
Some more sophisticated remote starter systems have a switch which fits in the antenna circuit - when the car is started with a key, the antenna in the ignition lock is enabled - and only when remote starting is the concealed transponder connected.
On some high security cars, e.g. Lexus, you can't even do this - the whole antenna system is completely enclosed, and the area around the steering column shielded, so that it is not even possible to attach a key to the steering column and have the transponder work.
In this case you have to use a rather less elegant solution. You need to get a locksmith to take a blank transponder key, and to program the transponder (as normal) but not actually cut the key. The result is a key that fits in the ignition lock, and has a functional transponder, but which will not turn. When you leave the vehicle you leave this key in the ignition, so that the remote start can operate, and when you want to drive, you just replace it with the real key, so that you can turn the ignition.