I think all I needed before he arrived (as opposed to wanted) was:
~Carseat (to take him home in)
~ pram/travel system
~Swaddle cloths x2
~Fleece blankets x2
~10 newborn baby grows (with feet & scratchmits at this time of year) - make sure they button up the front, as babies hate things over their heads when tiny and lying on poppers must be uncomfy
~Hats x3
~Cardigans x4
~cotton balls
~Change mat
~Old towels for change mat (so no cold plastic on bum)
~ 2 hooded towels for baths
~ 2 bags of nappies
The swaddles were gifts and I thought they were stupid and never planned to use them, as well as stuopidly overpriced (the John Lewis receiving blanket ones) but they were a godsend, he loved them. Lovely soft brushed cotton and so easy to use.
Secondhand is fab, babies grow scarily fast - everyone says that but it's mindblowing when they're yours.
Car seats & mattresses are dangerous to buy second hand, as knocks make the carseat pointless, and a mattress can harbour spores which are linked to cot death. I got a mattress protector from John Lewis on mine, and the mattress itself has an impermeable cover that comes off, too. BUT - all that ended up being pointless, because he sleeps with us. Which I swore would never happen. So you might want to get a moses basket or a travel system with a carrycot instead, for daytime naps, or until you know you aren't going to co-sleep for sure.
You shouldn't use anything but water on a newborn - they need a month to build an acid mantle on their skin. And actually, I only use wipes now when out, because cotton balls and water clean better - but I then put a barrier cream on his bum. We use Neal's Yard because we got 2 pots as gifts, and I have to admit it works a treat. But I'm sure Sudocrem does, too.
A sling can be a godsend with a fussy baby. You can wear them around the house, and they're happy and asleep. But I'd not call it an essential.