There is a little amplifier I am very fond of which I have used with dynamic mics. Since your coil situation is much like the one faced by someone trying to amplify a dynamic mic, I encourage you to try this circuit and see if produces a usable signal. Just replace the "microphone" (speaker) with your coil.
http://electrosuite.com/audio/bc547-dynamic-microphone-amplifier.html
The lower transistor acts as a common base amplifier, which is fairly unusual. It has a current gain of less than 1, but it does provide significant voltage gain. The upper transistor is in a common collector configuration, so it has essentially unity voltage gain, but the current gain is good. In short, this first amplifies the voltage, then the current, to give you a strong output signal. Although you will likely need a second stage after this, that should be much easier.
EDIT:
Concerning your noise issue, do you know where the noise is coming from? Sometimes I just have a power supply that's super noisy and ruining everything. I like low budget solutions, because of, well, my budget, so I usually test this by running the circuit on batteries. If things start magically working, then it's time to work on the power supply.
The EM brakes are normally designed for spring-set, EM-release operation. With that design, the brake does not release if power is lost or the driver circuit fails. For most applications, that is the "safe" mod of operation. To convert such a brake to EM-set, spring-release operation, it would need to be mechanically altered so that the direction of the spring force and EM force would be interchanged with each other. That is not likely to be practicable.
Since EM-set brakes are rarely used, you may not be able to find one that is suitable. You might find an EM operated clutch that is suitable for installation as a brake.
Best Answer
That coil will probably draw more than 1 ampere of current - I don't think your power supply is up to the job.
I'm going to go into "grouchy old man" mode and tell you to quit looking for stuff on youtube. It great for watching cat videos or old cartoons. It kind of sucks at anything that needs good explanations and details.
Try looking for education sites like this one that go into detail, and explain things.