Yorkie Splash and Shine is an all natural product. I stated using it when Gracie was about 10 months old. The owner has a facebook page so you could ask there if you want to make sure. Of course you never want to get any cleaner in you puppies eyes.
Yorkie Splash and Shine - Pet Supplies - Lebanon, MO | Facebook
There is a grooming section here on YT that has some good grooming tips and a few videos.
To start out you should have a metal grooming comb and a good set of dog nail clippers. I would never advise cutting your dogs nails by yourself. And if you have no experience doing it I'd take him to a groomer or vet tech at first.