1. Somewhere to sleep. cot / bassinet. I would buy secondhand cot but new mattress.
2. Car seat (often can wait till Target have one half price. I got mine half price at Target for $129)
3. Pram or good baby carrier or both! Check out Manduca or Ergobaby. I prefer when bub is little to just use a carrier, this way a pram can be purchased a bit later.
4. Linen - Blankets, wraps, face-washers. Target again have great size wraps. Plus they often have sales.
5. Clothing for bub.
It's easier for us to just bath bub either in shower with one of us or in the bathroom sink.