The problem is you need to change mirror sets for each wavelength, unless you want to buy a super expensive mirror set. I have 550$ in the required set in year 2000 dollars.
If you could find two Omnichrome 632 mixed gas high reflectors at 99.9% or better, you'd be all set for 430 to say 670 nm.
The reflectance of the mirror determines the FP finesse which is the resolution. Anything less then 98% reflective is not worth messing with. So your restricted to dielectric mirrors. The curvature is important too, You can do it with flats, but the required alignment is a pain in the A$$, so you can do Fabry-Perot and have cheap and great resolution, or do Michelson and have inexpensive, but pain in the butt to build over long distances.
Most people replace the mirrors on with a "V" folded mirror pair or a retroreflector for long distances to reduce alignment problems on the Michelsons.
The old saying cheap, accurate, or easy to build, pick any one or two, applies.
Steve