From your description of your previous experience with handguns, I think you answered your own question - get one with a thumb safety. I haven't carried an M&P with an external safety, but the ones I've handled did not seem as thought the safety lever was overly protruding. To carry any pistol comfortably, get a quality holster. Quality holsters go a long way to keep the gun rubbing uncomfortably against your skin, and quality holsters sometimes prevent unintentional discharges. Futhermore, proper training and regular practice while adhearing to the four rules of safety further aid in the safe and proficient handling and use of a pistol.

Police, regardless of what has been issued or authorized, have blown holes in police station walls, police cars, and other places not because the firearm did not have a proper manual safety, but because of some sudden lapse of judgement. The same thing has happened to civilians (although if a civilian was blowing a hole through a police station wall or a police car, there were other issues...), and to military, where the safe carriage of loaded firearms sometimes goes to the extreme based on a REMF's lack of understanding or other factors.... ADs have been around a lot longer than Glocks. I worked for an organization that allowed DA/SA Sigs, Glocks, and DA revolvers of Colt, Ruger, and S&W flavor. The ADs were pretty much evenly distributed between the three catagories.

I have carried Glocks for over 20 years, round in the chamber. I currently carry an M&P 45 full size in a Milt Sparks IWB, round in the chamber, no thumb safety. If the finger is off the trigger the pistol is pretty likely not to fire unexpectedly. Yes, things such as shirt tails, pull cords, and even junk holsters can get into a trigger guard and cause an AD, but as I said before, training and practice builds proficiencey and awareness...