There are many different opinions to answer your question. I recommend starting with a 4 channel Co-Ax. Some will suggest you skip the Co-Ax and go straight for what you described, 4 channel Single Rotor Fixed Pitch, which should be your second heli.

Think of your first heli as sort of a sacrificial trainer, which will probably have a few crashes and repairs. So availability of parts might affect your heli choice. Co-Ax is easier than Single Rotor, so you have a better chance of staying in the hobby, and not quitting out of frustration. Even Co-Ax has a learning curve that can be challenging at first.