I was on active duty until June 19, and then I joined the reserves on August 3rd. I'm wondering how I should enter my military service.

For purposes of the TurboTax interview, you "served in the U.S. Armed Forces in 2016" and your military status as of December 31 2016 was "Reserves". Also, you were "in the military all year".

As long as your enter your DFAS Form W-2(s) accurately and indicate that you "served in 2016". the program will ask all the relevant military questions necessary to identify any special tax issues. 

Whether you select "Active Duty Military" or "Reserves" (or "National Guard"), you'll get the same questions, just in a slightly different order. 

Please remember that you may have had a change in your state of legal residence. It stayed the same as your HOR until  you left the Marine Corps, but may have changed at that point.