I have tons of experience with kittens, newborn-6-8 weeks, as the local shelter contacts me when they are lacking fosters or space for the older ones and will be euthanized if I can't grab them.
So, here's some basics-
First thing is, go get KMR (kitten milk replacement) or other brand that the local pet supply store has.
This is essential to this kittens growth and developmental needs, whether it's you or another owner for it's life, and know if were not pulled from momma so early it would be happily nursing for weeks more than it was allowed. (how sad)
This baby will chomp on dry because of hunger, but will not take in enough with only dry, so you want kitten canned. 3x a day give the baby 1/3 of a small can such as fancy feast (KITTEN) which is more nutritious and higher caloric than adult.
As for the dry, the very best I believe is BABYCAT. Second is NATURAL BALANCE KITTEN FORMULA.
Always have fresh water available.
By the way, for so young of a baby, I find works ideal is keeping a low -sided litter box with non-clumping litter (never use clumping litter for a kitten) , a small bed/bedding and food and water dishes in a closed/small area. Not in a different room or it will not always go in the litterbox, when they get the urge to go, it must be right in their face so to speak for them to get in on time. They do not hold it for more than seconds before whoop, gotta go now!
Also allowing a baby of 6 weeks to roam free is overwhelming at least. They are perfectly happy to only be in 1 small area right now, then by 8 weeks will want a bit more space to roam and play.
My personal way is setting up a large carrier with a small litter box at the back, their bed towards the front and small dishes like a cut down paper cup taped to the front door. The carrier is kept on the floor with the door wide open during the day for easy access, and at night the kitten is put inside and the door closed, for safety, etc.
As for the vet visit, it needs the first FVRCP vaccination (not too young unless still with momma) and a deworming treatment. That's it.
Good luck, it's pretty easy really, just feels like alot when it's the first :)