"This Kind of War" by T.R. Fehrenbach to me at least, is the finest single volume on the US contribution/it's very strong on the big picture UN stuff (it discusses many of the other UN members who went, but doesn't go into like whole chapters on them). If you only did one book on Korea, this would be the one I'd recommend.

"Brothers at War: The Unending Conflict in Korea" by Sheila Miyoshi Jager is a very good overview of Korea pretty much from World War II to 2000's, and is one of the better books for getting the greater geopolitical perspective, and of being more recent vintage is also better able to discuss the various atrocities committed by all parties during the conflict (which is not to say the DPRK/China didn't commit the lion's share, just the ROK and UN did commit some bad acts that are usually not included in pre-2000's histories). Again, good book, and I think it's one of the better ones for getting a good comprehension of the conflict and how it fits into history

I found Max Hastings "The Korean War" to be a pretty decent one-volume book on the war.

Opinions on Hastings can vary, but he delves into a wide range of topics from front-line combat to the politics, from POW camps to the trenches. I found it gave a pretty broad perspective on the period and didn't rely extensively on prior knowledge.