I arrived a little after 8 on a Saturday for Shuffle Along and was 12th in line. Not the best position, but I did end up getting a ticket just fine. By the time the box office opened, however, there were at least 25 people in line and most of them didn't get tickets. It will probably be a little less crowded on a Wednesday, but to ensure your safety in getting tickets, I really wouldn't recommend getting there later than 8:30.
Typically, when arriving at the Lunt-Fontanne around 10:15, I've been able to get tickets just fine, so your odds of getting tickets to both the shows you want are pretty good. Not sure if Neverland does SRO, though.
The Color Purple has a pretty popular rush, and most people I know try to get there around 8 to be safe. Something Rotten and Disaster are quite a bit easier, I think, but I've never rushed either so I'm not completely sure.