My era, too. I was #107.
If your real question is what we did between the time we turned 18 and the time we were or weren’t drafted, we pretty much lived our lives. Some of us went on to college (or quickly decided that we wanted to go to college after all.) Some of us enlisted, either because we sincerely wanted to, or wanted to get it over with. The rest of us got jobs and waited to see if we’d be called up, just like our brothers had during the peacetime draft, our uncles during Korea and our fathers during World War 2.
At the height of Vietnam, the Marines were drafting, as well as the Army. The Navy and Air Force always filled their quotas through enlistments – mostly because you had a much smaller chance of being shot in the Navy and Air Force than in the Army or Marines.
RealityChuck and I went through roughly the same thing. When you turned 18 you went down to your local draft board office and filled out a form. They sent you a card. If you were still in high school, you were classed 1-HS until a few months after you graduated. If you were in college, you were classed II-S until you flunked out, dropped out or graduated.
If you weren’t eligible for any kind of deferment (there were a lot of classifications beyond student and conscientious objector,) you were classed 1-A and you waited for your number to be called. The lottery gave you a better idea about your likelihood of being called up, although if the local pool of draftees was small, the board would call higher and higher numbers until it reached its quota. During the peacetime (post-Korea, pre-Vietnam) draft you were never quite sure if you’d ever be called. With the lottery, you were grouped by year. If your number was called, you got a physical and were given a number of other tests. Assuming you passed all of them, you got your notice to report. If you weren’t called during your year, you probably wouldn’t be called at all.
The “Army, Army, Army, Marine” thing was actually a joke from World War 2. My father told it to me. For that matter, it might have been a joke from World War 1.
One thing you need to remember is that the services filled their quotas through the draft, NOT by activating members of the National Guard and Reserves. In those days, a lot of servicemen filled their military obligations by serving one or two years on active duty, and then transfering to a Guard or Reserve unit. I guess the idea was that it would be unfair to rotate them back into active duty. That made for the unintended consequence of those with connections being able to enlist directly into the Guard/Reserve and avoiding active duty.
The Sole Surving Son exception didn’t include being drafted (you could still be assigned to a non-combat role) and it didn’t extend to brothers being assigned to combat. Also, it wasn’t automatic – you had to ask for it.