Nowadays, instead of thinking about particles and waves, for QM, I focused on the mathematical construct the state vector or density operator. Since time evolution of a state is deterministic (despite measurement is probabilistic) , this makes the state vector somewhat more "tangible"and hence I can "stick my hands in to manipulate it". The maths (modulo the careless mistakes I made in some linear algebra concepts) of QM then become slightly simpler and
I can start sort of reasoning with quantum problems semiquantitatively