When to start potty training?

My son will be 2 next month. We've had a potty chair for a few months now, and he's gone in it probably 3 times, but we haven't really started pushing it yet. I'm due with our 2nd child in July. What I'm wondering, is should I start pushing it more before the baby gets here or after? I'm concerned if we start now, he'll see brother in diapers and think he needs to be also. Or will it work to tell him diapers are only for babies? I've never been around other small children, so I have no idea where to start lol. He tells me after he poops, and sometimes after he pees. He's also starting to stick his hands down his diapers, so I'm hoping that will stop with the training as well. Thanks in advance!!