Energize!
Go to Warp Factor 1.
Report!
All hands man battle stations.
He's the captain and therefore part of the military, and even when aboard a starship, military-like commands will be used frequently. Kirk is very direct. When he wants information, he simply commands "Report" and his fellow officer will give him the information he wants. A great example of this action takes place in "City on the Edge of Forever" when Spock is building the tube-based tricorder attachment that will allow the tricorder to work in the 1930s. Kirk walks into the flat and sees the complicated tube circuit board complete with Jacob's Ladder and says "Report." If it were me, I would have laughed and said "What the heck is all that?"
We don't see the crew in their off-duty clothes much in TOS. I remember we saw Uhura once wearing a bizarre flowing dress, but offhand, that's the only one I remember. Seems to me that with 430 crewmembers, a third of them at any given time would be off duty (a 24 hour day would have three 8-hour shifts of varying crew). We should see off-duty crew walking the decks of the Enterprise in their "civvies." But we don't. I'll have more thoughts about this in my "Crew Recreation" section.