DS branched QM. Once you graduate you go to Ft. Lee VA for Logistics BOLC (LOGBOLC). LOGBOLC covers Quartermaster, Transportation and Ordinance branches. You go through LOGBLOC with your branch specific peers, but you will learn aspects of all 3 branches.
It is likely early in your career, regardless which of 3 the branches you slot for, that you will wear the hats of any one or more of these logistics based branches. The unit you go to will likely determine which hats those would be. for example, if you are QM going to an Aviation unit, you probably wont have much cause for a transportation role. There are tons of unknowns until you get to your actual unit after LOGBOLC.
That said, when you get ready for Captain, you will attend "Logistics Captains Career Course" where it really becomes about Army logistics and sustainment.
My son LOVES it, great people, interact with all levels of command. Best of luck.