Hey there. It is hard to work with a bub at home. I started my PhD when DS was 3-4 months and ended up with terrible PND from all of the pressure of trying to do both. I deferred and restarted at 12 months which was more realistic for us. Using a sling so he is on you may help him to sleep a little more and also give you some hands-free time while still spending time with him. But I have to say the more alert they are of their surroundings the more they want to be played with rather than just being with you.
I think I actually have a baby play book at home which I don't need. It is in a well loved condition but has great activity ideas for babies from birth to 1 year. PM your addy if you like and I can hunt it down. You should be guided by his behaviour as to when he is happy to play by himself and when he would like some company. Babies just like experiencing different things and places, such as different tactile objects, musical things, toys, trees etc.
HTH