You have gotten some really good advice. I will second all of it. I sent mine to a well credentialled reining trainer last fall-he is nowhere near finished, but, has a good enough handle for me, since I have no intentions of doing anything big with him. His training was actually hindered by the fact that he was not STARTED in reining. Like NRHA said, what you consider broke may not be at all what is needed for reining, and, in fact may take longer to reining train because they have to REtrain.
Here in the east, I would not go to a reined cowhorse trainer unless that was what I wanted to do. Reining and reined cowhorse are not the same, around here. Similar, yes, but you will not win at the same level reining as you would with a horse trained by a reining trainer. JMHO.
I also recommend going to shows, watching and learning. You will see trainers you will NOT want on your horses, regardless of their level.
Yes, it is definitely more cost effective to buy a made reiner than train one. I can only say that my guy has 6 mo with a trainer who does reining but not a true "reining trainer" (since I didn't think I could get a true reining trainer to take him as he is grade)and another 7 months with an excellent reining trainer.....and it is $800/mo. I could have bought a really nice horse.......
A friend has one she bought from a trainer as a 3 yr old, started late.....but also started fast, so had some significant holes in her training....she has added another 12K in training to her, so again-between what she paid, and what is invested.....could have had a made horse.
The people are great, it is a ton of fun, and worth every penny.