Navy you can't really go wrong, but gray can easily be a trap. If the red is a true red (as in fire-engine type stuff), the grey absolutely has to be dark, almost approaching charcoal. If the suit is mid to lighter grey, burgundy will work wonderfully. But a mid to light grey suit with a bright red tie is one of the worst things there is in my opinion.
I think I'd say that you need as much darkness (or lightness) in the tie as you have lightness in the suit. So bright fire engine red is fine with a charcoal suit, but as the suit gets lighter the tie should go towards burgundy or pink to work.
But if the suit is dark enough, it's fantastic. Either with a white shirt for that dramatic bold contrast, or with a pink shirt for a softer expression.