Dave G.:
We should start Cha-Cha on beat 1 with a prepare side step either on LF or RF. Then followed by a backward basic or forward basic.
Most of us probably learned Cha-Cha with forward basic (count: 234&1)and backward basic (count: 234&1) first without the prep. step. Note that this way we are missing the starting (1) count which is the heavy beat of the measure. After you can handle the steps, your instructor then added the prep step in your case.
International style instructors will insist that you start with a prep. step in your first lesson. But anyway, in your second case: put your 100% weight on your RF (Right leg straight, Left leg straight, no weight, big toe touch floor) to start, and do a quick shift weight on to LF on the heavy beat 1. It should be a strong and quick move to make it look sharp. Then immediatly follow a RF backward basic (234&1).
I hope this is helpful.
Dave L.