Definitely start buying nappies, wipes and toilettries (baby bath, shampoo etc) now.
The best shower gift I was given was a huge laundry basket FULL of this stuff and boxes of nappies. We didn't have to buy nappies for her first two months, and the baby bath and shampoo only ran out recently (DD is 19 months old)!

We are stocking up on all that stuff already for this baby because it was wonderful to never have to worry about it running out the first time.