I attached the tape-head directly to an oscilloscope, without any amplifier, besides the highest scaling/amplification available on the oscilloscope.
For the hall sensor I was using an amplifier, but it was not enough. The noise was amplified as well, yet still no signal to be seen (for the cards I tried). And I wanted a good alternative.
I'll make a simple op-amp amplifier for the tape-head and report back. A suggestion for a suitable hall sensor would still be nice.
Regarding frequencies, I have no specific requirements yet (exploratory phase), definitely nothing higher than audio-frequency, probably well below that. It might be however that the magnetization on the cards/stripes is not that strong.
Edit: the tape head is from an old cassette recorder, so it can read and write onto audio tapes.