Basic supplies needed for your new puppy are a kennel, bed, leash, harness, collar, food and water dispensers, puppy diapers (there is a difference between gender styles), potty pads, and toys. You can buy any brand of supplies that you would like, but it does help the puppy adjust to their new home if there are some familiar aspects. You do not need to buy these specific things but hopefully this will give you an idea of what you will need.
Here are a few of the things that I like to buy for my dogs. I get most of my stuff from amazon.
Bed:
https://www.amazon.com/AmazonBasics-Double-Door-Folding-Metal-Crate/dp/B018YCTH7W/ref=sr_1_1_sspa?s=pet-supplies&ie=UTF8&qid=1510160521&sr=1-1-spons&keywords=dog%2Bkennel&th=1
https://www.amazon.com/dp/B00QHC05FU/ref=twister_B00QHYFFGM?_encoding=UTF8&psc=1
Potty Training:
https://www.amazon.com/IRIS-Puppy-Dog-Training-Holder/dp/B00JPZDV0W/ref=sr_1_7?ie=UTF8&qid=1510159917&sr=8-7&keywords=puppy+pads
https://www.amazon.com/Buddy-Super-Absorbent-Training-Puppy/dp/B01M1C4BTQ/ref=sr_1_4?ie=UTF8&qid=1510159917&sr=8-4&keywords=puppy+pads&dpID=41tAdyQCWYL&preST=_SY300_QL70_&dpSrc=srch
Diapers:
https://www.amazon.com/Luxja-Reusable-Diapers-Washable-Purple/dp/B071H9NJFT/ref=sr_1_2_sspa?ie=UTF8&qid=1510159994&sr=8-2-spons&keywords=puppy+diapers&psc=1
https://www.amazon.com/Luxury-Reusable-Dog-Diapers-3-Pack/dp/B00UPEW4AA/ref=sr_1_5?ie=UTF8&qid=1510160032&sr=8-5&keywords=puppy+diapers&dpID=51%252Bkn8qQ9DL&preST=_SY300_QL70_&dpSrc=srch
I line the diapers with sanitary napkins
Food/Water:
https://www.amazon.com/Aspen-Pet-Bistro-Gravity-Feeder/dp/B009NVA5J8/ref=pd_bxgy_199_2?_encoding=UTF8&psc=1&refRID=PXHNQXE9R4XEYR56E70G
https://www.amazon.com/Aspen-Pet-Bistro-Gravity-Waterer/dp/B009NV9FMG/ref=sr_1_9?ie=UTF8&qid=1510160234&sr=8-9&keywords=water+pet+dispenser
Leash/harness:
https://www.amazon.com/PetSafe-LSH-3-8-X-6-RED-Nylon-Leash/dp/B000OGLI60/ref=sr_1_4?s=pet-supplies&ie=UTF8&qid=1510160320&sr=1-4&keywords=leash+for+small+dogs&dpID=41IA7dAcSUL&preST=_SX300_QL70_&dpSrc=srch
https://www.amazon.com/Voyager-Weather-Best-Pet-Supplies/dp/B00M0V7RWQ/ref=sr_1_4?s=pet-supplies&ie=UTF8&qid=1510160345&sr=1-4&keywords=small+dog+harness&dpID=51ejLV-gezL&preST=_SY300_QL70_&dpSrc=srch
