Grooming…
I have been a dog groomer for 25 years. Lucky me, right?

ALL dogs shed or lose hair, some just more than others. I guarantee you can find someone allergic to ALL breeds of dogs, hypoallergenic, non- or low-shedding breeds withstanding.
Cats are the worst; they are covered in their own saliva. You can teach a dog not to lick-personally, I am not a huge fan–neither of my dogs lick–we taught them when they were young.
Weekly baths? Yes, but ONLY if you are using good shampoo and feeding a great dog food. I would also add Omega-3’s, available from your vet. Good allergy shampoo is also available from your vet. Side note: Furminator shampoo and solution/conditioner are the BEST for shedding out a dog. I go through tons of that stuff.
Bathing removes the naturally occurring oils, and this can make a dog scratch, and scratch, and scratch if done too often…try to maintain a happy balance; its individual to the dog. Generally, weekly baths are harsh on a dog’s skin, and you could cause skin problems if it isn’t done correctly.
The best advice I can give for a good bath is RINSE, RINSE, RINSE.
Also, Allerpet does work. Follow the directions, or find a groomer that will do the treatment for you. I use it for my customers all the time. I would also consider purchasing (or finding a groomer who uses one, probably a better idea) a high velocity dryer. If used properly, a HVD used BEFORE and AFTER the bath will blow out dirt, dander, loose hair.
Congratulations on your new puppy; you have a very positive, responsible outlook on this; I wish your family the best.
Melissa