I think all the advice so far is good solid advice, the basics of how weathering stages are carried out. When I think of black myself compared to lifecolour Panzer grey I dont see it working, Raw umber will. The pz38t is a minefield of rivets, so heres my opinion and its just me, no need to destroy a model because of my input.
Lighten the pz grey with grey, not white it will just turn grey, sounds odd but trust me.
Get your washes in as you see fit.
Heres where I would go different, before going to final weathering pastels etc. take Tamiya flat earth and thin down by about 80% to 90% and lightly wash in to the model, after it drys you will notice a very dusty finish, like the diry that never washes off in the real world.
Terry.