Intersting..I'm 5'11" 170 and wear slacks and a dress shirt, no sports jacket, so I am in exactly your shoes, so to speak. I also work in Dallas, for an added coincidence.
In any case, at work I use a smart carry. I believe I could get away with a tuckable IWB, but I can draw faster from a smart carry than I can with having to untuck my shirt, and then draw. Also, the chance of the clip being seen is too high for the setting I am in.
You can't go wrong with a smart carry, but if you haven't purchased your gun yet, you could also go with a small keltec or some other pocket gun. A good pocket holster with a small single stack compact pistol should disappear in a pocket, even in slacks. My normal carry is an XD9 subcompact in a smart carry, and it's comfortable all day, I can access it fairly quickly, and nobody is the wiser.
With your type of setting, I would either go pocket carry, or smartcarry.
Also, be careful, about half of of the hospitals in the DFW area now have a legal 30.06 posted. The Gov is trying to change that, but I doubt that will happen for a long time.
And welcome to the forum!