I've never openly welcomed a pimp... but welcome to the forums!
I'm glad you already have the Copperband in there. After that, I agree to put the tangs in there at the same time, or the smaller one first. I would add the most aggressive, Powder Blue, last and would use Ca1ore's advice on introduction (except I like to QT regardless since they are so prone to ich). I'm not one to mix several Yellows together in 150 (assuming 72x18" footprint) and they will still have a pecking order that could lead to issues but you may want to wait on others with experience of having 3 together. Rather, I like to mix the tangs that come from different genus. You could throw a Kole or Tomini. I've never had the Pyramid but would, as long as it works with the CPB and your corals, I would add it sooner than later. The Maroon is personal choice. They can be quite territorial and do get large. It is a fish that typically goes in early because they are so hardy but are probably better suited for going in later and it may not allow the Anthias too close. Now would be the time to decide between keeping the Maroon or swapping it out for some Percs. The Anthias is a tougher one. If you are going with a more peaceful species like the Lyre-tail, then I would add those early to make sure that they're getting enough food (probably 3-4 times a day). If you are going with Bartlett's, which can be snippy, you may want to add them towards the end but before the Powder Blue.
Since you are new here, take a good look through the tank forums to get ideas and ask as many questions as you have. Try to post them in the most appropriate forum to get the best and most responses. But take your time because nothing good happens fast in saltwater!
Hope this helps and good luck
Mike