So you bought a new kitten, now what?

First of all, you need to know that the food they have been trained on here is Purina One Healthy Kitten (dry food). Now.... You feed your kitten whichever food you like, but you may need to transition slowly, by adding half and half, or something, to avoid upset tummies. 
The kittens here, have been trained on non-clumping clay litter. This litter is ALWAYS sold in a bag. You can switch to whichever litter you like, but it's still helpful to know the litter that they have been trained on. Chunky litter like I use, helps to keep it from sticking on their tiny paws. Also imagine if your kitten decided to munch on clumping litter, it would clump up inside of their throat. Other customers have success with yesterday's news litter, or other options. My adult cats use clumping litter, but not my kittens. 
Your kitten will need a short litter box. Do not start them out on a big tall lidded litter box with a door. They will most likely not use it. The kittens are trained on litter pans, which are short sided litter boxes with no lids. After they get older, then sure, you can switch them to larger litter boxes... with lids or doors or whatever. 
Also, your kitten needs to be able to keep warm, so please provide them a cuddly bed, such as a cat cave bed. They will no longer be able to cuddle up next to their litter mates, so a cuddly bed will help to keep them warm. 
Make sure your kitten's water dish is non tippable. Find something with a flat heavy bottom, and make sure they get fresh water, daily. 
All of these suggestions are only tips. You do what you want with your kitten.
Here is a link to my Amazon Kitten shopping list. Maybe it will give you some ideas:
www.amazon.com/hz/wishlist/ls/34X17XTZXM0P0?ref_=wl_share

Make sure your kitten gets it's second round of kitten shots by the age of 12 weeks.
Make sure you spay or neuter your kitten by the age of 5 months.

For baths, I just use the kitchen sink. I hold the kitten under warm running water, keeping the head dry. I only let the water pour from the neck down. (You can use a wash cloth to clean the head).
I use original blue Dawn dish soap if the kitten is really grimey. Otherwise, I just use Johnsons Baby Wash, or any cat shampoo. My white cats use a special purple cat shampoo. 
After I rinse the kitten off, I wrap them up like a burrito in a towel, leaving only their head sticking out. That's when I use a warm damp cloth to clean the head. Usually focusing under the eyes, the chin, and the ears. After removing all of the dirt, I spray their face with Meow Mist  , and then I wet a rag with alcohol free witch hazel, and wipe their pretty little face down again. If the kitten needs eye drops, I might stop and drop a few saline drops or Visine in their eyes. Then I dip a corner of my rag in rubbing alcohol and wipe down inside the ears. 
If the kitten has long fur and I find they are having a hard time keeping poop from getting stuck around their little booty, then I will get about 1/4 tsp of coconut oil and rub it around their little area back there. It really helps to keep the poop from getting stuck on the fur. 
To clip the nails, I use those cat nail clippers that look like scissors. I wrap them up in a towel like a burrito, and fashion it to where only one paw is sticking out. I put on some reading glasses and get under a bright light, and clip their little fingernails, that way. After you finish the one paw, then poke another foot out, and wrap them in an inescapable burrito again, and so forth and so on. A kitten really responds to a high pitch voice, and sort of a baby talk. Just let them know they are doing real good and looking real pretty. It helps put them at ease during bath time.  Anyways, after you're all done, you can put them in a wire crate and set a blow dryer on low. You can either sit there and hold it, or prop up the blow dryer in a heavy vase or something, like I do.  Make sure they are not in a crate with very little ventilation, or they will get too hot. It really needs to be a wire crate. You can also hold them and blow dry them by hand. Always keep the setting on low. You don't want to burn them. Or... if nothing else, just cudle them up in a blanket and cuddle them until their dry. The point is, you do not want them to catch a chill, or get sick, which is what will happen if you just set them free to run around with wet fur. Use a metal comb to brush out long hair kittens. You can refer to my Amazon list for examples.
By the way, if you buy dog sweaters for your kitty, get a size XXSmall. They do not do good with hoodies, so try and stay away from those. 
We do not have a problem with fleas here. I usually put Borax in my mop water. We have switched to complete ceramic floors, so I do not have carpeting anymore. A great thing to use is food grade Diatamaceous Earth. You can sprinkle some in their food, or around their bedding if you ever notice fleas. It is basically a type of sand, so it is safe. If added to food, it will also keep your kitty worm free. Another thing I add to my adult cats' food bucket is probiotics or Acidophilus. I add other things, too like Uva Ursi, Echinicea, horsetail, and many more herbs, but I do not feel like looking up all the spellings. 
I also wanted to tell you that you can find cute pet supplies at surprising places. Five Below has a fun selection. They have many beds to choose from, and they're only $5.55. Wow. They have lots of blankets, toys, clothes, tunnels, etc. At times, they even have scratching posts. Another place is TJ Maxx. They have a bigger pet bed selection than Petco or Petsmart. I think Walmart has $5 beds, not as cute, but... hey your cat don't care. Target has some extra cute cat houses. I am always checking target.com for the latest cardboard cat scratch house. I also check Ebay and Amazon for novelty cat supplies. At Dollar Tree, they have litter boxes. They are kitten sized litter boxes, too.  They also carry cat dishes, a few toys, and clay non clumping litter. I usually do my weekly shopping for my kitten supplies at Tractor Supply and HEB. I have Instacart bring me my kitten food and kitten litter from HEB. Specifically I order the Tidy Cats Instant Action non clumping litter in a bag that costs  $4-something.  I don't scoop my kittens litter box, but instead, I dump it all out and pour in fresh litter. HEB always has their food in stock, when other stores are always out of it. Again, the food I am using is Purina One Healthy Kitten dry kibble. I DO NOT USE Purina Pro Plan. My kittens did horrible on it. But for whatever reason, they do awesome on Purina One.
​I do not feed my kittens wet food, but I'm sure you may want to. So if you wanna know what I recommend, it is Fancy Feast KITTEN in a can, in chicken flavor only. Turkey would be choice number 2, but never fish flavors. Also I have been known to give my kittens what is called "Kitten Crack". Do you want to know what it is? It is Gerber or Beech Nut baby food in a jar in the flavor of chicken and gravy. Your kitten will shake as they eat it because it is SOOO good to them. The animal rescue service use this food to catch feral kittens and that is where I heard about it. Kittens cannot resist it. 
Ok, sure sure you will want to buy what your vet is pushing, and that's great. If they say grain free, I mean, go for it. I purchase a food that I have found is easily digestible for my kittens. 
For years I used Royal Canin Babycat, but during the epidemic, they went through a supply chain issue, and so it led me to search for a different food. I think they are back on track now, so if you want to use Royal Canin Babycat, whether wet or dry, I think it is a good choice, too. If you can't find the Babycat, then get the Persian kitten variety. I didn't like the plain Royal Canin kitten. I mean, my kittens didn't like it. I didn't try it myself, but you get the picture. 
​Ok, nice talk. I hope I gave you some good information, or at least some good ideas. Comment below if you have any suggestions for me, or anybody else who may come across this blog. Thank you.