There is a virtual library published on the Viet Nam conflict. The following are some personal picks that I have find helpful. I have deliberately not included personal accounts as they are simply overwhelming in numbers. I would suggest reading in several of these titles and then when you start to feel familiar with the basic outlines of the conflict to start reading some of the first person accounts. Some such as 'Once a Warrior King' are as good as the best writings that came out of the World Wars.
The first citation is for the e-books file for Viet Nam for the US Army Center for Military History. It will lead you to most of the Army's Viet-Nam Monographs and some other selected publications. These volumes were written or the writing was overseen by a senior officer with relevant experience in the conflict with the subject examined. As the title says they are monographs examining specific aspects of the Army in Viet-Nam such as artillery or air mobile, or special forces operations. They are not a bad place to start. The writing tends to be dry but a lot of information is presented. Unfortunately the series ends chronologically about 1969. The Army's official history program has been lame as to publishing the projected 15 plus volume series projected on the Army and the war. Two volumes on the advisory effort, one on communications, one on the operational narrative for 1966 and one volume on the Army and the media are all appearing so far. The Marines, on the other hand, have completed their entire Viet-Nam history series. It runs to about 10 volumes and is comprehensive but presents a compressed factual operational narrative on an annual basis. The USAF and USN have also publsihed a number of volumes on the war. The Air force besides publishing operational narrative volumes has produced a series of interesting monographs on such areas as air base defense and defoliation operations.
I have included two general histories of the conflict; Herring and Karnow. Both are written from the establishment liberal viewpoint. Of the two I prefer Herring as it is a straight forward introductory history and covers the whole war.
There are no books specifically on the diplomatic or political background. There are a number of these dealing with Johnson ad the politics of the war. There is only one book on the French phase of the war Fall's book on Dien Bien-Phu. I would also recommend his 'Street Without Joy' which is episodic but brilliant and covers aspects of the war the French fought from 1946 to 1954. This book is also of interest as it was originally published in 1959 and just about every US Army officer and many NCO's seem to have read it part or completely as part of their preparation for going to Viet Nam. I first read it in 1964 in high school and found it to be literally a book I couldn't put down.
I fear I have slighted the air war and naval ops in this list. There are a number of good books on these topics one I do recommend is "One Day in A Long War" which describes the multiple naval air operations around hitting some important targets during the spring 1972 campaign.
Let me know how you find the books you sample.
http://www.army.mil/cmh-pg/online/Bookshelves/VN.htm
Bonds, Ray. The Vietnam War: The Illustrated History of the Conflict in Southeast Asia. Salamander Books, Limited, 1999.
Braestrup, Peter. Big Story: How the American Press and Television Reported and Interpreted the Crisis of Tet 1968 in Vietnam and Washington. Boulder, CO: Westview, 1977.
Coleman, J.D. D. Pleiku: The Dawn of Helicopter Warfare in Vietnam. St. Martin's Press, Inc., 1989. ISBN: 0312914687
Fall, Bernard B. Hell in a Very Small Place: The Siege of Dien Bien Phu. Da Capo Press, Incorporated, 1985. ISBN: 0306802317.
Glassner, Ronald J. and Ronald Glasser. 365 Days. George Braziller, 1986. ISBN: 0807609951
Herring, George C. America's Longest War: The United States and Vietnam, 1950-1975 (America in Crisis). McGraw Hill College Division, 1996. ISBN: 0070283931.
Hosmer, Stephen T., Konrad Kellen, and Brian M. Jenkins. The Fall of South Vietnam: Statements by Vietnamese Military and Civilian Leaders. Crane Russak & Co., 1980. ISBN: 0844813451
Karnow, Stanley. Vietnam: A History. Viking Penguin, 1997. ISBN: 0140265473.
Krepinevich, Andrew F. The Army and Vietnam. Johns Hopkins University Press, 1990. ISBN: 0801836573
Lanning, Michael Lee and Dan Cragg. Inside the VC and the NVA: The Real Story of North Vietnam's Armed Forces. Ivy Books, 1993. ISBN: 0804105
Lee, Alex. Force Recon Command: 3rd Force Recon Company in Vietnam, 1969-70. Random House, Incorporated, 1996. ISBN: 0804110239.
Lee, Alex. Utter's Battalion: 2/7 Marines in Vietnam, 1965-66. Ivy Books, 2000. ISBN: 0804116385.
Lewy, Guenter. America in Vietnam. Oxford University Press, 1980. ISBN: 0195027329
McMaster, Herbert R. Dereliction of Duty: Lyndon Johnson, Robert McNamara, the Joint Chiefs of Staff, and the Lies that Led to Vietnam. New York: Harperperennial Library, 1998. ISBN: 0060929081
Miller, John Grider. The Bridge at Dong Ha. Annapolis: U.S. Naval Institute Press, 1996. ISBN: 155750587X.
Moore, Harold G. and Joseph Galloway. We Were Soldiers Once - and Young: IA Drang , the Battle that Changed the War in Vietnam. 80th Edition. Harper Trade, 1993. ISBN: 0060975768.
Moore, Harold G. and Joseph Galloway. We Were Soldiers Once - and Young: IA Drang , the Battle that Changed the War in Vietnam. 80th Edition. Harper Trade, 1993. ISBN: 0060975768.
Moore, Harold G. and Joseph Galloway. We Were Soldiers Once - and Young: IA Drang , the Battle that Changed the War in Vietnam. 80th Edition. Harper Trade, 1993. ISBN: 0060975768.
Nolan, Keith William. Battle for Hue: TET, 1968. Presidio Press, 1996. ISBN: 0891415920.
Nolan, Keith William. Death Valley: The Summer Offensive, I Corps, August 1969. Presidio Press, 1999. ISBN: 089141665X.
Nolan, Keith William. Operation Buffalo: USMC Fight for the DMZ. Bantam Doubleday Dell Publishing Group, 1992. ISBN: 044021310X.
Nolan, Keith William. Ripcord: Screaming Eagles under Siege, Vietnam 1970. Presidio Press, 2000. ISBN: 0891416420.
Nolan, Keith William. The Magnificent Bastards: The Joint Army-Marine Defense of Dong Ha, 1968. Dell Publishing Company, Incorporated, 1996. ISBN: 0440221625.
Sorley, Lewis. A Better War: The Unexamined Victories and Final Tragedy of America's Last Years in Vietnam. Harcourt Brace & Company, 1999. ISBN: 0151002665
Spector, Ronald H. After Tet: The Bloodiest Year in Vietnam. Vintage Books, 1994. ISBN: 0679750460.
Stanton, Shelby L. Rise and Fall of an American Army: U.S. Ground Forces in Vietnam, 1965-1973. Presidio Press, 1995. ISBN: 0891415769.
Stanton, Shelby. The 1st Cav in Vietnam: Anatomy of A Division. Presidio Press, 1999. ISBN: 0891416862.
Summers, Harry G. On Strategy: Critical Analysis of the Vietnam War. Presidio Press, 1995. ISBN: 0891415637
Warr, Nicholas. Phase Line Green: The Battle for Hue, 1968. Ballantine Books, Inc., 1998. ISBN: 0804118698.
West, F.J., Jr. The Village. New York: Harper & Row, 1972. ISBN: 0553293443.
Zaffiri, Samuel. Hamburger Hill: The Brutal Battle for Dong AP Bia, May 11-20, 1969. Presidio Press, 2000. ISBN: 0891417060