He's in a new territory with a new person. Cats are more territory oriented than people oriented. Purring can be a sign of fear as well as happiness (though not as common), and because he plays with you, I'd say he feels safe with you.
He should be confined to a room you spend time in - like your bedroom (unless he's not going to be allowed in there later) until he's comfortable in the space. When his territory is "set" and he has his safe space to run to, he can be allowed to explore the rest of his territory. For some kitties this is a few days, for some a few weeks.
Either way, I'd do a few things to help him adjust to all this "new-ness."
Whatever room he's confined to initially, spend as much time in there as you can. Drag the laptop in there, fold your clothes in there, iron things in there - whatever you can. The sole attention doesn't always need to be on him - but you should be around him. Also, having a very regular schedule for when you scoop litter, put out new food (or wet food), change his water - whatever it is - really helps. Also, knock lightly on the door before you go in - let's him know what's happening.
Also, you said he likes to play with you. Just make sure you're playing with a toy - do not let him think hands, arms or feet are toys. You will really regret this later.
Just sitting in there and reading out loud or singing while you do stuff is great. Also, even though he already feels comfortable with you, you can get some t-shirts really good and sweaty. After a play time, put some treats down for him on one of them. Put the other one under his food dish. This will reinforce his idea of you as safe and a good thing.
OH - because he's already comfortable with you, maybe put one down on a cat bed for him to help him feel more secure when you're not around.
When letting him explore the rest of the space, I'd already have another set of food and water out for him wherever you're going to be keeping it. And I'd have another litterbox out somewhere for him - with one cat, you should have two litter boxes anyway. And little kitties sometimes get excited and need to have a litter box near so there won't be an accident.
I'd also have some scratching posts out for him - though one should be near where he sleeps. Cats love to stretch and scratch when they wake up, so the best place to have scratching boards or posts is near or right next to where they sleep to help protect your furniture. Maybe have a cat bed or two out with posts next to them. He won't know their his at first, but he'll figure it out.
So... then when he's going to be allowed to explore, just open the door, don't take him out. Let him explore on his own - initially, supervised. See how he reacts - or if he even leaves at first. Judge whether or not to leave the door open permanently on how he reacts. If he just bolts out of the room and hides somewhere, it's a little too soon. Let him hide for a while - and get the feel for the new smells and sounds outside of his room. Just go about doing whatever you were going to do - after a while, put him back in his room. As a kitten, after a couple of days of this (if it even amounts to that) he'll probably be out and around, exploring, or curious about you and what you're doing.
Or, after a little time, maybe try drawing him out with an interactive wand-type toy. Just make sure you never leave them out where kitty can accidentally access them. They like to chew the string, and if they eat it, it can get wrapped around their intestines and require surgery.
Also, talk to him a lot and use his name a lot. This will help him learn his name.
And as he grows and needs to learn what is OK and not, "talk" to him in his own language. If he's doing something he shouldn't, hiss at him and blow a short, sharp puff of air in his face and say sharply "No". You're talking to him in a gentle language he totally understands - and he'll learn the meaning of the word "no," which may, at some point in the future, eliminate the need for the short, sharp puff of air in the face.
Also, remember that when he's around 4 months old he'll begin teething. He'll be very "bitey" - if he goes for fingers, hands, ankles or toes, definitely do the puff of air in the face, say "no," and walk away - OR give him something appropriate to chew on and then totally ignore him. Make sure he learns that bad behavior gets him NO attention. And to meet his need during teething, we found the best thing is a box of bendy straws scattered throughout the entire house. These make great chew toys when they're going through that "need to chew" stage, and they can't be ripped into little pieces they eat.
Here's a great article for someone with a new kitty: http://www.thecatsite.com/Care/18/Br...a-New-Cat.html
Also, there are more great articles you may find interesting (these are located in the links provided in the boxes up at the very top of the page next to TheCatSite.com logo) :http://www.thecatsite.com/Cats/Cat_Behavior.htmlhttp://www.thecatsite.com/Cats/Cat_Care.html
Enjoy the wonder of being owned by a kitty!
Hope you feel better soon!