oh your pup will shed. I have a long haired and a stock coated GSD. I find that the long hairs get tangled together and do not fall onto the floor. I brush him every night and get handfuls of fluff. It is also a good time to check for scratches or bugs that you can't otherwise see. My stock coated gal's hair just gets loose and falls so I have much less hair on the brush from her. I only wash my dogs when they get smelly, which means only a few times a year. This summer it was so hot and humid out that my long haired boy decided he liked the shower! Most of the time I'd simply rinse him off with cool water with a hand held sprayer (make sure you have a really good drain screen). Big thirsty towels were a must since everything was wet once he got out of the shower.
For my dogs, I spoil them and give them treats throughout the brushing process. When my boy was a pup he thought that brushing was an invitation to wrestling. Took quite some time to convince him it wasn't.
Yeah, we live in the same state. It was hot at times. (I actually thought the last few summers were hotter and more humid.) But for me, it was the constant rain we got this summer that brought out the smells. When he got wet, his natural odors came out more. While I wanted to wash him, it wasn't worth it because he was always wet from the rain. What I like about this pup is he's short haired or stock coated as you put it. He's much easier to dry off than the previous long haired one. His coat really does "shed/repel" water while the old guy was like a sponge.
On a side note, around 2 years of age, I started saving the hair/fur from (brushing) the previous dog until he died. Managed to fill up 1 whole lawn sized garbage bag of about 10 years worth of his hair. I had read about ladies who had made blankets, scarves, hats, etc. from dog's fur.
One more thing I wanted to add for the OP....some dogs love the brushing. It feels good to them. If your dog is one of those, it's another opportunity to bond with it.