From Primary the cadet moved to Basic and flew the BT-13, 14, or 15.
Multi Advanced had AT-9, 10, and 17, with some B-25, B-26, and A-26 dual thrown in later in the war.
Then it was off to four-engine transition training on the B-17 or B-24 (or a B-25 or 26 transition course if that was where they needed you).
Next was Combat Crew Training and Phase Training before heading to a combat zone.
This is simplified and I know I'm missing some aircraft types, but it gives a general idea of the steps.
A B-17 pilot friend of ours told me of his training at the Advanced Multi School at Pampa, Texas and the fearsome AT-9. His was the first class that was restricted to flying the AT-9 only with a qualified instructor--absolutely NO solo flight for students due to it's unforgiving nature. Too many had busted their a$$es in it. He did say it was fun to fly until you retarded the throttles, and then your eyes widened pretty quickly.