I was home for just over 4 mos and started pumping at 1 month. Those first few weeks I wanted to get my supply in line. I just got a few oz every day (pumping ~1hr after dd's first daytime nursing) that I would freeze because we were still together 24/7 and nursing on demand. I kept that one pump session in the morning plus pumped 3x a day at work for a few months, then I decided the morning one was too time consuming plus I had 500+oz frozen, so I now only pump while at work. Some days I just barely keep up with her, other days I have an extra 6oz to freeze.
Honestly, I think this answer is different for everyone and there is no necessarily right answer.
For me, I BF and pump throughout the day. During the time I am watching her, which is almost the entire day, I breastfeed her for feedings and pump either after or inbetween feedings to increase supply and have milk for my H to feed her during the four hour nap I take once a day.
I pump about 10 oz. a day, and approximately 2-4 oz. goes to DD during my nap. I have 6 oz. containers, so I put one away every day. You can only keep refrigerated milk for so long, so after I have filled my six oz. container, it goes straight to my deep freezer. It can last in there for 12 months, so I'm not worried about starting too early.