Congrats on your baby!!!!
You should start getting your pup familiar with brushing teeth so I would say to get any small sized baby toothbrush and also C.E.T vanilla mint toothpaste.. your pup will love it! Mine gets her teeth brushed every day before bed and she loves it, lol.
Virbac Animal Health C.E.T. Enzymatic Toothpaste | Pet Toothpaste
For grooming, I think the Chris Christensen wooden pin brush is great for brushing and detangling gently.
Wood Pin Brushes for Pet Grooming, Show Dogs & Cats
I have the small pink one and it's my favorite brush!
I would also recommend the Espree plum perfect face wash and small baby face cloths for when your pups face needs a washing, lol. It smells great and washes out easily.