Which methods have worked best for pursuing a graduate degree after commissioning?

There are several ways to go about this. Some branches offer a masters program with the advanced course.

When I arrived at the LOG career course I put myself though a masters with UMUC on-line. I used TA for it. No regrets. I am glad I went on-line as I PCSed 3 times and had one deployment.

I also found a program with Central Michigan University for a Masters of Science in Administration (MSA). They grant 5 classes (15 credits) from ILE towards the MSA. I used my tax exempt funds from the combat zone to pay for the remainder.

Since you are a LOGI consider applying for TLOG which is a masters program in Logistics

To answer your question about time. In my PL days (1999) I did not have reliable internet. But I was doing a lot of correspondence courses. If technology was more advanced back then I would have started graduate school earlier. I comes down to how you balance work, life, family, school and so on.

Best of luck.

What is your branch? Branches that can and do attend the Maneuver Captain's Career Course are given an opportunity ti apply for a Master's Program through Columbus State University. This would stabilize you on Fort Benning for an additional six months following MCCC, IF you fall into that category.

At ILE you are required to earn a Master's degree if you do not already have one.

Or you can go the old fashioned route and pursue a Master's while serving in your respective area. I would recommend getting it knocked out as a lieutenant as opposed to waiting until you've been promoted to Captain. It's difficult but not impossible.

I waited until my second assignment at the 6-year point to work on my first MA. I used my VA benefits to cover the tuition. Mississippi State University offered on-base classes. I PCS'd after I had completed 2 semesters and finished up with Webster University through on-base classes at my new assignment. Check with your installation education office. My daughter completed her Bachelors Degree in accounting through Phoenix on-line and was pleased with the experience.
I know there's lots of choices now that weren't available in the 1980s and 1990s, so a combination of on-line and on-base classes might work best for you. You should seek advice from your chain of command, also. They can advise you on the necessity for an advanced degree to help ensure promotion. I see you will be a prior-service officer, but I'll remind you anyway: the most important job you'll have as an officer is the one you have now; do it well first.