You're doing great. The fact that you care and are worried about screwing up speak volumes.
Babies are lazy. Milk doesn't come instantly. It takes a little work on their side to trigger a letdown. Bottles are immediate. A lactation consultant may help, not sure if that's already something you've tried. Some babies have a terrible latch so it can be super painful for the breastfeeding parent. There are tongue ties and there are lip ties. Both of my kiddos had mild lip ties that didn't cause pain most of the time. The site kellymom was super helpful to me in the early weeks. Just ignore the super strict stance on BF-only. Just go for the tips.
Your wife is doing great. Do things for her, don't just ask her what she needs and do it. Do things proactively. Bring her water, snacks, a blanket, etc.
I forget what brand it was, but one of those fancy bamboo ones I think? The diapers are just white. The only way to tell front and back is by the tabs. I had a free sample. Did not purchase more.