You probably wouldn't bring home a baby without some amount of preparation, so you shouldn't bring home a puppy without preparing.
Some Questions that need answering:
Where will the puppy sleep?
Where will the puppy eat?
Where will the puppy go out?
The answers to these questions also provide a basis for the gear you need.
The number one answer to sleeping should be a crate! The location of the crate is up to you. I always have young puppies in the bedroom with me - it's much easier with a young puppy to have them there. You can get mats and beds that fit in the crate but honestly old towels are best for young puppies- much easier to clean up as necessary but still comfy.
They can eat in the crate as well - although I usually have two crates so one is in the bedroom and one is out in the kitchen. They need some bowls for food and water, and you need some puppy food. You should ask the breeder or shelter what they have been eating so if they know you can keep them on the same thing and make any changes to their diet slowly.
To take the puppy out you need a collar and leash. Granted the collar can wait until you have the puppy and can measure- you will get an adjustable collar - they will grow out of it but it should last a couple months. Also I advise getting an id tag made up in advance. Although some pet stores have a machine in house that stamps tags right there.
You may want to get doggy pee pads to line the crate and or an exercise area- much easier to clean up than newspaper (and who has newspaper anymore). With any luck you wont get a puppy like my LeeLoo that shredded the pee pads often.
You should also have some puppy training treats on hand right away- I like very small soft treats for training there are a bunch of brands you will need lots.
You need cleaning supplies - I use natures miracle, lots of paper towels on hand.
You need things they can chew on and a chew deterrent. "Bitter apple" is the deterrent of choice to spray on furniture etc. (you probably wont use it till they are older since a young puppy shouldn't be able to get to anything to chew it.) Chew toys are a necessity, rope chews, sturdy "stuffed" (unstuffed) toys are great. NO RAWHIDE.
I also always get my puppies a stuffed animal friend. I love the Snuggle Puppy with a heartbeat!