The magnetism on tape is proportional to record head current, not voltage. And our starting point is flat recording. So the basic record amp is a constant current source or an output impedance much higher than the head's inductive impedance at the top of the band. You could drive constant voltage and pre-compensate; that's usually the Hard Way.
The wound playback head is a differentiator. Your basic playback amp is an integrator.
Since it is hard and unnecessary to have infinite DC gain, a Spec tells you to use a pole around 50Hz.
Since there are a dozen reasons treble falls off, a Spec tells you to add a Zero, typically around 3KHz.
The playback head could be wound for any impedance. Inductance changes with turns, capacitance mostly doens't change. In audio heads, a low impedance gives a low voltage and amplifier noise voltage can be an issue. But a high impedance head will have a self-resonant L-C peak and drop. For very wide response, you use the lowest impedance which will overwhelm amplifier noise voltage. For economy design, you wind-up until you see the peak (or until winding costs rise), and shift it to compensate some other droop.
Same thinking applies to phono and guitar pickups, and input transformers. All windings work the same; differences are physical size (capacitance and wire cost), expected response, and cost of amplification.
These will almost never "require" FET impedances. And historically FET noise voltage has been higher than a good clean BJT. Most tape heads are wound to work fine with BJTs.
But with half-good design and semi-modern parts, tape noise will overwhelm all other noise sources. You always have a hiss when tape is stopped, you should have a lot more hiss when tape rolls. So don't bang your head on amplifier noise.
The playback head has an infinite null where gap length equals recorded wavelength. No cure. Your tape head designer picked the gap for the application. This is one reason we throw in a ~3KHz Zero. We may have another +/-3dB tweak in the last half-octave of the band.
At this point you should be able to play a Reference Tape perfectly well aside from LF bumps.
You can check head and preamp response by injecting a small signal across a 1 ohm resistor spliced into the head groundy lead. It should trace your NAB/IEC curve up to some reasonable top-of-band point.
There are many more losses; these are compensated in the record side. For 30ips you might just rise the top octave 6dB and be very happy. For 1.7ips this would give dull voice recording; cassette record channels have huge resonant peaking at the top of the band. Many decks don't fudge below the ~50Hz pole, but you can boost if you want, if you average-out the subsonic noise which ultimately limits linear tape.
You really want to upgrade an existing amp+heads set, NOT work totally from scratch. Even if you will replace all the electronics, note all the signal levels and impedances before you trash it.
For total from-scratch: set up your playback first. Play standard tape, adjust gain, check response and see if you screwed-up. Except for finding a gain which brings standard tape level to standard patchbay level, and verifying that amp-hiss is lower than tape-hiss, this should be trivial.
Record is tough with mystery heads. Inject a signal a decade away from the band ends. 400Hz is habitual for audio. At low levels it will be distorted, ignore that. Bring it up until the peaks flatten. Note the level. Trim the azimuth. Raise frequency a few octaves and re-trim azimuth.
Come back to 400Hz. Back-off a good chunk, 10 or 20dB. Add bias, at least twice your hoped-for HF band-limit. Up to a point, playback level increases (and that low-level kink goes away); after that, it erases signal faster than it averages-out the lo-level kink. Note this level. But now go an octave down from the HF limit (which will be a matter of judgement for a from-scratch design). Again increase bias for maximum playback output, and a little more to make signal fall a bit ("overbias"). The lowest-THD condition will be slightly overbiased, but the maximum bandwidth is with maximum output bias. You pick your compromise. It is easier if you want 15KHz response at 30ips than it you demand 20KHz response at 1.7ips. Oh, and high tones at slow speeds saturate the surface of the tape; we traditionally test at -20dB, but hot rock drum tracks exceed -20dB in the top octave, so again you compromise.
Having found a good bias, run frequency sweep and bump-up your top (and maybe sub-bass) for flat response. For any economic recording speed, this will need a resonant circuit with more than 6dB/oct slope (however such steep slopes are dubious for sound quality).