I've got one that age right now. They must have been born about the same time. I've raised many cats, all strays/rescues. Here are some guidelines.
Do not let him go outside if you can't afford to pay lots of medical fees. They can pick up a lot of nasty diseases and injuries. When the weather changes the like to lie on the road if they are out at night. That's why you see so many dead cats on the road at those times of years. They also get fleas and worms. In the country, or a cat who is desperate to be outside, it can work but they need a lot more medical care.
He should be neutered in about a month, at 4mos old. Call your vet to see if you need to make the appointment ahead of time.
He should already have had some shots and will need some more later, more if he's going outside.
Flea collars are useless. Get Advantage flea drops. They aren't cheap, but they work. You will also need to flea bomb your house, and yard if the cat's been outside. They get into the upholstery and yard. It pays to be thorough when there are a lot of them, otherwise you fight a loosing battle. Once the situation is under control flea drops every 4 mos is enough. The drop should kill eggs and adults, and be placed on the back of the kittens neck. Get the right dose for the size of your cat.
Don't let him bit you in play. He won't respond to being told "no" but if you always use toys to play with him and never your body he can learn not to bite or scratch people. He will do some scratching.
Do not get his claws removed. They do this by removing the whole finger. This is horribly abusive. Even doing the front paws only is horrible. They can never walk right again and many never adjust psychologically. They will be prone to accidents and all sorts of joint problems. It's cruel. If you can't handle the scratching you shouldn't have a cat. Most cats will outgrow most scratching by 12 mos old. Most will confine their scratching to a good scratching post if it's provided.
6 months is too late, and 4 weeks is way to early to neuter. If you wait too long he'll begin to spray in the house to mark his territory. Once he starts he'll never stop and you will either live in cat pee or he'll have to live outside. If you do it too early he won't develop properly. 4 MONTHS (give or take a little) is the right time. Talk to your vet.
Congratulations on your new family member. Cats are amazing pets. They get rid of mice, keep us company, make us laugh, lower blood pressure, and ask very little in return.
There are so many stories! Sterling is into everything right now. He's so awkward and wipes out all the time. It's a good thing he only weighs about 3lbs or I'd probably have a broken nose. He's constantly running into my face while I'm sleeping. Just typing this he's been across the keyboard several times. Now he's playing with my hair.