When you're going shopping for a new puppy, it's very easy to get overwhelmed with all the things that you find in a pet store.
A lot of times this leads to buying things that you don't necessarily need. First and foremost you're going to require some sort of confinement area, for a puppy in particular, this can really help with potty training, but for adult dogs also, they need to learn a little bit about your house before they just get free run of your living room.
This is an exercise pen, and this is a god example of what would be considered a long-term confinement space. Also, you're going to require a crate of some kind. Whether it's a wire crate, or a closed-in travel crate are also fine. And then toys, I would look for things that you can stuff food into, such as Kongs, or hollow bones. Something that the dog can use his mouth and his energy to work the food out of. I'll sometimes replace a high energy dog or a puppy's food bowl with a hollow toy that he can dissect food from. You're going to require a nice, soft, comfortable bed, that you can encourage the dog to sleep on, instead of your couch, or your bed. These also give the dog a safe place and a comfortable place inside his crate to sleep on.
Don't forget, you're going to require water dishes and a travel bowl possibly, also. That's really a good starting point for what you are going to require. Those are the necessities. There are a lot of cute, fun things you can get also but, that's where I would start for a shopping list for you dog.