What schools do officers attend to get promoted?

BOLC, CCC, ILE, War College. Probably others I'm not aware of

CPT career course, ILE, SAMS, War college

Actually it's schools and other pedigree items that make an officer somewhat but not completely competitive for promotion. It varies by service, branch, designator, etc. However, for each officer, there is a progression path with various beans that should be accumulated and at what rank. There are the stock in trade leadership courses. Masters degrees start to come into play when going up to the O-4 board. Professional credentialing for varied staff corps is likewise prevalent at the O-4 level. Credentialing in varied National organizations can be a good bean if it applies to your designator. Even so, liken this stuff to skating the short program. To be competitive, you need to skate the long program as well. Performance, initiative, taking care of people; the list goes on. Then it's having competent raters and reviewers who know what they're doing. There's a lot of urban myth out there regarding "magic pills", letters to Boards, etc. Work diligently on all the pedigrees and your job. Promotion through O-3 is pretty much assured. But really pay attention to O-4 and above as it starts bottlenecking quickly. Learn about the promotion process, boards, and the various documents that are published. Key one would be the Board Precepts that get revised every year. And if you get a chance as a mid grade O-3, listen carefully to what senior officers who actually sat Boards previously have to say. That's a fairly small group. I did around 6 promotion, continuation, command Boards in my time. I still cringe at stuff members post on this forum.