As reflected in PP's posts, every baby is going to be different in its preferences so it's not really possible to say if (for example) a bouncer will be pointless for you. Ditto every mother is different - one person may find something essential because she's pushed for time or has particular family/domestic arrangements, while another woman never uses that same thing.
We got almost everything free from a family member who'd had all her kids, so had the luxury of trying lots of things out without worrying about wasting money if they weren't right.
My personal experience is that DD loves the vibrating chair and it's been a lifesaver - giving me 10 minutes to eat breakfast, for example.
Sling is great, but get one that's designed to spread the weight and give you good back support or it'll ruin you.
Love our bath support hammock thing, inexpensive from Mothercare and it makes bathtime easy. Ditto baby bath. Saves water and time running a little bath, and DD is (at just 6 weeks) too big for the kitchen sink.
For me, a breast pump is essential. Expressing means I can get more than 3 hours' sleep at a time. It has kept me sane. Doesn't need to be expensive or electric, mine is a slightly knackered old Tommee Tippee hand pump. Works fine.
Microwave steriliser. 6 minutes and you're done.
I personally find washable breast pads great, but having said, that I don't leak much. If that's you, I recommend them. Plus you can save money in the long run. Little Lamb do good ones. Buy enough for a week, week and a half and bung them in with the normal wash.
Things I don't use:
Towels with special bits on (clips to go round your neck, little hood to go over baby's head). Normal towel is fine as long as only baby uses it.
Scratch mitts
Toys. DD will be interested in them later I'm sure, but right now the sight of me crinkling up a plastic bag is the best thing ever. She doesn't care about the special 'newborn toys', bar her black-n-white fabric book.
Parasol for pram. Drives me nuts, useless unless I am stationary and there is no wind at all. Muslin, bit of clothing or pram shade cover is just fine.