The three Tangs you have mentioned are all from the genus Acanthurus. Typically it is not advisable to keep Tangs from the same genus together because their body shape is similar, and they see this as a threat. Adding them at the same time may help with this...temporarily, but most likely not solve the problem, long-term. Sometimes it can work, but most times it doesn't.
When mixing Tangs, it is usually best to avoid similar body types and similar colorations among them. Picking them from different genus's usually works best.
As far as the "Powder tangs", they are more prone to parasites than other tangs, for some reason. Tangs in general are already prone to ich, these Tangs are even worse.
For the Achilles, these are considered a difficult fish to keep because they usually don't do very well in average systems. They are basically considered expert only, and do best in very large, established tanks.
Sorry to be the bearer of bad news, but I don't think those 3 Tangs, in a 125, would fair well.
