Instead of looking at the Pokemon actually in the games, or the individual 17/18 types in the game, I decided to tackle the most coverage against the 171 possible type combinations, with no effective weighting. I also made a distinction between whether or not Freeze-Dry and/or Flying Press are available, and whether maximizing supereffective or 4x effective is preferred, all combos with these maximized have full neutral+ coverage. Everything was brute-forced via Python.
The numbers are total super effective targets, 4x effective, 2x effective, 1x effective, 0.5x effective, 0.25x effective, and 0x effective.
Freeze-Dry and Flying Press, super eff. prio.:
Freeze-Dry Ground Rock Fairy - 157, 29 128 14 0 0 0
Here are the 14 types this combination is not super effective against: Grass Steel, Ice Ground, Flying Steel, Bug Steel, Normal, Psychic, Ghost, Fairy, and any of the 6 combinations of those 4 basic types.
Freeze-Dry and Flying Press, 4x prio.:
Freeze-Dry Flying Press Ground Rock - 154, 36 118 17 0 0 0
Freeze-Dry, 4x prio.:
Freeze-Dry Fighting Ground Rock - 152, 35 117 19 0 0 0
Flying Press, 4x prio.:
Ice Flying Press Ground Rock - 148, 32 116 23 0 0 0
Neither, super eff. prio.:
Ice Ground Rock Fairy - 150, 25 125 21 0 0 0
Neither, 4x prio.:
Ice Fighting Ground Rock - 144, 31 113 27 0 0 0
Pre-Fairy, super eff. prio.:
Freeze-Dry Flying Press Ground Rock - 142, 36 106 11 0 0 0
Ice Fighting Ground Rock - 133, 31 102 20 0 0 0
In contrast, here are some of the worst 4-type combos:
Normal Flying Press Poison Bug - 77, 13 64 74 18 2 0
Grass Poison Bug Fairy - 91, 10 81 61 17 2 0
Normal Fighting Poison Bug - 84, 14 70 73 12 2 0
