As young as he is this young, no need to worry about schedules at all at this stage. If he is healthy and a good weight I wouldn't wake him if he is sleeping well, he will let you know when he is hungry. If he goes longer then three hours then maybe if you want him to sleep more at night then during the day. He will sleep a lot during the day at this age though. Some babies are different and sleep longer right away, others need fed more often. Lay him down too in a bassinett in the living room now too to get him used to sleeping with noise. That will save you big time later.
You kind of follow his cues right now.
If he is on the smaller side he needs to eat more as it doesn't stay with him that long. My daughter was very small and ate every two and a half hours until she started solids at 5 to 6 months, then it was every four hours, then it was six hours then at around the year mark she would do a 8 hour stretch! :) My son was a larger baby and could go three hours with each feeding until five months, then it was five hours straight then it was all night at around 10 months.
At 6 mos you can start more of a schedule, two or three naps during the day at the same time each day, lay him down for bed at the same time. He will figure it out. When he is older lay him down awake and teach him to fall asleep himself, that will help you a ton if he wakes at night and can fall back to sleep.
After 6 mos don't rush to him at the very first noise you hear, make sure he is truly ready to wake up and needs something. They wake several times a night and the difference is if they need you truly or can go back to sleep themselves. I never did crying it out until my babies were over 6 mos.
Hang in there and relish the newborn stage. I miss it so much. As sleep deprived as you are it does truly go by fast. Just lot's of love and cuddles and enjoy it. It gets easier as each month goes by, promise and CONGRATS! :)
Try laying down when he does, don't worry about the things in the house right now, you need your rest too.