I could write a separate list for both my babies - each is so different, and each parent is different too. I know I look at some of the prams and think they'd drive me mad for xyz reasons but other people love, love, love them.
Both babies essentials have been the bouncer (I also got an auto swing this time, but it doesn't send DS to sleep but the bouncer does), a pram that you can steer one handed, wondersuits and a baby monitor (though I thought I wouldn't need one both times but have).
I also find a change table a big back-saver.
This time I didn't let anyone talk me out of a capsule like I did with DD. I don't care if he grows out of it after a few months, those first couple of months are so hard and I've lost count of the number or times I've been soooo thankful to have it these past 9 weeks. Just make sure to get one that also rocks when on the floor.
I would get the bare essentials at first. You will get given so much, especially things like blankets, play mats, toys etc. Things you are unsure of either hire, borrow or get second hand (which typically can be sold on at the same price).