The image quality differences between FX and DX associated with sensor size are minor. In particular, there is no difference between DX and FX in background blur; there are tiny differences in depth of field in some circumstances but unless your requirements are highly specialised you can get any depth of field you want with either. The only exception is that if you do a lot of photography in very low light FX may be a better choice - but both DX and FX will allow you to get excellent pictures in far less light than you could with film.
There are some differences in AF, notably in the fraction of the viewfinder covered by AF points, so if you use tracking AF a lot DX may be the better choice. However, if you are comparing the digital options to film-era memories the difference between 5 AF points on the F100 and 51 on the D7200 is far bigger than the difference between the spread of 51 points on the D7200 and 51 on the D750.
Lens choice is the real issue, IMO. If you want wide angle primes (other than fisheyes), FX is the only choice. Even if you don't mind a zoom, DX offers limited wide-angle options and the FX options are better and/or cheaper if you want wider than 24mm equivalent. Conversely, if you use long focal lengths a lot DX is the better choice unless your pockets are deep.
CX is over-priced, and Nikon seems to have lost interest in it, but if rock-bottom size and weight is a very high priority, and you want good tracking AF, and you can find a good deal, it is an option to consider.