Repelling a magnet from a coil
Think voice coil from a loudspeaker, they've already solved the efficiency problem.
You will have therefore a magnet assembly with an annular gap, with an air-core coil into the gap.
If the coil is a lot longer than the gap, you have good linearity with insertion distance.
With any practical annular gap, the MMF in the magnet will be dominated by the permanent magnet, and little affected by the levitation current.
Now which to have fixed and which moving? If the coil is fixed, then the moving magnet would be very susceptible to forces from stray and varying external magnetic fields, and even moving lumps of ferromagnetic material nearby. A moving coil solves that problem, at the expense of getting current into and out of the moving coil.