I'm by no means an expert, but you can start on the 2,3 (rock step), then go to the side on the 4&, then left foot to the side on the 1. I'd count it this way too, or think 2, 3, cha-cha, 1. I don't like it when teachers count the 4&1 as cha-cha-cha because it sounds like each 'cha' is the same amount of time, and it's not. The first two are in one beat (4&) while the last cha is the first beat, which is a whole beat. IMHO, it's much easier to start on the 1 beat going to the left side.
As for rumba, in int. style, I start on the two (rock step) because it's easier I think. I did American rumba before Int. and it's usually counted as Quick-Quick-Slow, so I find it easier to start on the Q-Q (rock step), and side step for 4, 1.
In american style rumba, you do a box for the basic, so it's very different from cha-cha.