Wills is a good one.
As soon as I found out I was pregnant the first time, I started putting the equivalent of a daycare payment ($1,200 a month for us) into VTSAX. It moved it out of the budget so we could see if there would be much impact. That pregnancy, we sadly had a 29 week loss, but had an excellent addition to our savings, we kept it up, and we had adjusted our budget so well that by the time our take home baby arrived, we actually didn't need "that" money for daycare and kept the payment up. I'm pregnant again, so another $1,200 has been going to VTSAX throughout the pregnancy. It will be re-routed to daycare once this baby arrives though.
We also did life insurance for me, as I wanted a higher policy than what work provides (1.5x salary). DH already had insurance. I'm glad I did it early in the pregnancy, as I later got gestational diabetes, and despite not being diabetic in normal life (or in my first or third pregnancy), that would have raised my rates!
The other big thing I'd say is to resist buying stuff. Babies just really don't need it. I returned nearly everything I got at my showers, and figured I could rebuy it if we came across the need. We never rebought the bouncer, swing, rock n play, exersaucer, bumbo, diaper genie, video monitor, or nearly any clothes. We just didn't need any of that (clothes seemed to appear like magic through size 2T). And I used the returns gift cards to buy diapers. The things I couldn't live without are some things people tell you you don't need: a glider and a changing table (both were free hand me downs from a neighbor). So people's styles vary, and I wouldn't get something just because it is on a list!
I agree with taking the time to organize YOUR stuff. I never nested with organizing baby stuff (mostly because we barely bought any), but it was good to declutter OUR stuff.