I dont think you must overdo this with neutering already. Dont hurts if it is done, especielly if your resident is allowed to go outside, but NOT necessary because of his new young pal.
You ask about vaccinating the new one before he comes:
HOW necessary, depends on, I would say.
But usually it is good to have your cats vaccinated, thus the newcomer too.
Most important distemper + cat flu, and rabies in some countries. There may also be other shots.
It depends also on how it is. CAN the new one be one week extra where he is? for example with mom? Are they and his old milieu healthy?
Breeders, for one example, do always take all the shots before they deliver the kitten. They also guarantee the kitten is healthy, thus a good breeder never deliver a kitten with a flu and the kitten is always vet checked.
But if necessary you can do all this including the shots when he is already with you. After the shots keep the kitten separate a couple of days: new milieu, new pal who is not yet pal, and dizzy after shots is much. Better to let him be alone.
Likewise. If the kitten comes from unsure milieu; you are not sure if he is healthy at all, keep them separated - a quarantene - at least one week.
In the time make a vet check up, the shots, deworming. You also observe and see if there are any traces of disease or something.
And you and the little one get friends, you becoming his new Daddy/Mom.