And I think short coils with huge diameter is the better choice...
A very important point.
The signal is proportional to the area and the number of turns.
For a given length of wire, we can have smaller area but larger number of turns. Or, a larger area and fewer turns. Because the area is square of the linear dimension, it is better to have higher area and fewer turn for a given length of wire.
But the source of the signal is also important; it should also cover a larger area (the OP says that the source produces a faint signal from a distant slowly varying magnetic field).
I agree that shorter length coils are much easier to handle; the largest coil diameter consistent with practical considerations is the best solution.
To reduce noise, I suggest that the coil may be wrapped with Al tape (reduce high frequency signals).
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Am after somewhere in the nanoTesla range variation/disturbance. Something like detecting a train passing a mile away...
Earth's own magnetic field is in the microTesla range. Small variations (around 1%) in the local magnetic field is easily measurable. That gets you to the nanoTesla range...
If you look at the B-H curves (I have not looked into) you will notice that using mu-metal at low magnetic fields have no gain; the gains are all at high magnetic fields.
By the way, how much magnetic effect (change) you expect to see for a train passing 1 km away?
If you want to use a mu-metal core, you may have to bias it with a permanent magnet so that the operating point is close to the rising part of the curve...