Broomtail Wrasse are, and get, very large and unless it's very small a 125 FO is too small for it. Also you can't keep very aggressive fish with it, as they will bite out pieces of its tail and could kill it in the long run.
That being said there are a number of fish sold as the Broomtail Wrasse, it would help if you posted a picture of the one you're interested in.
This fish does get pretty large and even though it maybe ok for now, in a 125gal FO tank, you're going to need a large tank down the line. On the positive side they do tend to grow somewhat slower. I wouldn't keep it with any very aggressive fish, like a large Grouper or an aggressive Trigger. Also you're going to need to give it some caves or openings in the rock where it can hide. As for a diet, lots of meaty foods like shrimp, squid, clams and fish.
It's a nice fish, pretty hardy and unless you keep it with some very aggressive it will do well for years to come. Some Broomtails are more colorful than others, especially at small sizes. Some have the Purple lips, Red Head and the blue/purple dots at smaller size while others don't look as nice. A lot has to do with the size and if they're turning into males.
The most important thing is that you're happy with the fish, after all it's your tank. People get caught up getting and keep rare fish instead of getting things that they like.
Do a search on the internet for some pictures and you'll see how they vary in coloration.