I would start now. My daughter is a week old and we've already gone through 2 packs of newborns. We had a diaper party and we got so many diapers. Thats an idea you can try
If you're having a baby shower you should do a diaper raffle! Its when you ask your guests to bring a pack of diapers and if they do they get entered into a raffle to win prize baskets. That's how I'm doing it and that way I'll have different brands to try out and if the baby doesn't like them or they don't work well it isn't a huge loss on my part.
I started right away will all sizes and different brands. Wipes also . If yu have a store like sams club around yu their prices on the bigger sized diapers (2+) are decent. But I know they are WONDERFUL prices on wipes. The one buy my house the best deal they usually have is a box of wipes 800_810 count for 20$
I started when I found diapers on a great sale or on clearance and was able to use coupons on top of the sale/clearance price so I was able to get them for about 10 cents per diaper when they normally cost 18-24 cents per diaper. I was still in my second trimester when I first bought and now have about 11 packs under my bed waiting to use any day now...
I'm a FTM too @35 weeks, my mom told me it's better to buy a small pack of different brands and varieties because the baby might not respond well with some brands. My brother got rashes with pampers and there's other babies who can't wear another diaper brand except pampers.