I think second time around I probably wouldn't need anything. But things I didn't use the first time: moses basket (my daughter slept in it once for 20 minutes, then we used it as a toy basket for the next 2 years, finally gave it away a few months ago), clothes that aren't vests/sleepsuits for the first 3 months (beyond that we started to dress her more in actual clothes, but really the first few months it was just sleepsuits day and night), I also don't think you need much in the way of toys for the first 3-4 months. Babies just like to be held. They don't really need to be entertained. We also didn't use a carrycot (didn't have one either). We either wore our daughter in a wrap (moby wrap is a godsend!) or if she was in the puschair, we just kept her in the car seat (she was never in there hours on end so wasn't an issue to make sure she lied flat).
Things that I think were absolute must haves though: moby wrap (seriously, a sanity saver), lots of muslins (we still use them daily and our daughter is 3), and if you plan to bottle feed, an electric steam steriliser and maybe even the perfect prep machine (didn't have one, but if I was to bottle feed at all next time, I would get one).