Which is the most cheap way to measure currents of this magnitude?
Could I use a toroid and pass the wire in the middle of it?
Shunt resistors are not good, since the Power is too high!!!
Current transformers are too big/expensive...
One usual way is to use a series resistance. These are called shunts. They drop about 100 mV or so at their rated full current. They are sold by instrument companies.
I would avoid making your own current transformer if this is an audio or lower frequency. If you must, use a tape wound core which has higher mu.