Perceived wisdom is to run a slightly shorter crank on the road bike than on your MTB. The theory being that it will help you to spin a higher cadence better and give a little more pedal clearance in the corners.
Of course though, it doesn’t really matter that much. It’s mostly personal preference. I prefer 170’s on both road and MTB, I like to spin and I prefer more pedal clearance on all my bikes. I’m 5ft10 but with reasonably long legs at 33″ inside leg, so my optimum length (according to the crank length calculator) would be closer to 175 anyway.
At 6ft, running 175’s isn’t going to be detrimental to you I’d say, unless you’re freakishly proportioned. If you are a spinner rather than a cranker though (or want to get better at spinning) then maybe go slightly shorter.
Chainring size wise… Unless you live somewhere pan flat, or can keep up with Cat 1 and 2 roadies already, go for a 34/50 compact.