John,
This is a great question for the dancetalk message board.
Where you start a dance and where a particular figure is thought to begin are not necessarily the same. For example, in Int'l style Waltz, some of the figures begin with the left foot (eg Reverse Turn, Whisk), while the others begin with the right (eg Natural Turn, Chasse from PP, and so forth).
If you have a preference for starting a dance with a step on a partiular foot, you either need to (1) start with a figure which also begins with that foot, or if you want to begin with a figure which doesn't start with the usual foot, (2) begin with a "prep step" to free up the desired foot. In the end, though, it is not necessary to confine yourself to one particular starting foot. The idea that one must always begin with this or that foot is really just a helpful tool for beginners, and nothing more.
You can begin Cha Cha with either foot and step in almost any direction. The trick is to simply shift one step to the side to ensure that you and your partner are on the same page. If you shift to the left, you will have your right foot free to start. Likewise, if you shift to the right, you will have your left foot free. With the left foot free, for example, you could begin the dance (1) on count 2, starting with the forward rock, (2) on count 1, starting with a side step to the left, then back rock on counts 2,3, or (3) on counts 4&1, with a side chasse LRL. Or you could begin with the right foot and do the opposite. That gives you 6 possibilities of ways to begin dancing Cha Cha, and that's just for the chasse basic. There are almost infinite possibilities for starting the dance, if you begin with a different pattern.
When we decide how to present a figure in our syllabus, we don't bother taking into account which foot might be more typical to start the dance with. What's important to us is to define the beginning and end points of the movement itself. And in Cha Cha, we believe that most figures begin with the rock step on the man's left foot. The right foot "prep step", which is not actually technically part of the figure, is included merely to demonstrate how it connects from the previous movement. It also gives you a way to begin on count 1, since the figure itself does not.
There is nothing wrong with starting the dance side on your left foot, then stepping back RF into a back rock. You'd still be dancing a Cha Cha basic. But in terms of the way we've laid out our syllabus, that would be considered starting the dance with the second half of the basic. It's no more "right" or "wrong" than starting a Waltz back on your right foot into the second half of a Left Box (Reverse) turn.
Regards,
Jonathan Atkinson
www.ballroomdancers.com