The most useful thing I bought for my first baby was.......

[bradleybecky]

?

Tummy tub
Muslins
Swaddling blanket

Reported the above post.

Babycook machine for homemade baby food, it's definitely a lifesaver after 6 months.
Before that a bouncer or a chair that the baby likes, I tried 3 different ones until he found the one he is comfortable to stay in.

Poddle pod
Breastfeeding cushion
Gro snug

A full set of very good quality cloth nappies. They have lasted through all three of my kids and are still going strong on DS (1 y.o.). SUCH a good investment (in terms of pocket and in terms of the environment).

Do you know what else? A good dressing gown and slippers for you, the mother. Because whether or not you like it, you will spend A LOT of time in your dressing gown and slippers. You'll need something to throw on in the middle of the night when it's cold. And first thing in the morning when you're serving your children weetabix five years down the line.

I know it's grim thinking about dressing gowns but by god, I've worn mine every single day for the past six years since DD1 was born.

Do not, I repeat do not, buy a fancy changing bag. What you need is a great big over the shoulder bag that you can open with one or no hands and dump loads of stuff in.

Talking of sleepwear, my suggestion is actually no dressing gown and no pjs that look like pjs. Instead invest in a nice wool wrap or smart wool long cardigan, and wear leggings and long sleeve plain top without 'sleeptight' written on it. That way you look semi smart and can pass as being dressed even if you aren't if anyone turns up unannounced

Initially:
Lots of sleepsuits (DS1 was rarely in clothes until over a year old)
Angelcare monitor (not video but with sensor mat - meant I was less likely to run up to check his breathing every few minutes!)
Swaddle - discovered it a little later than ideal but still very useful and now being used for DS2
Wedge shaped changing mat (useful now as DS2 has managed to roll onto his side from 4 days old )
Nappy bin
Beco baby carrier - one of the best for a bad back and very comfortable on the few occasions DS1 would go into it! Here's hoping for more use with DS2!

Slightly older:
Jumperoo - DS1 loved this and would happily stay in it for ages
Peg perego reclining high chair (bought for us as a gift) - quite expensive and I was a bit when we were given it but it is brilliant; comfortable, multiple settings / heights and reclines almost completely flat so newborn can lie in it (and DS1 when he has his morning milk)
Philips avent steamer blender - fantastic for those early purees!

Oh and agree completely with comfortable pjs! I bought a set of quite expensive maternity pjs after DS1 and am so glad I did! I practically live in them

For baby:

Sleepsuits/vests/babygros: tiny clothes are fiddly and uncomfortable - DS lives in onesies!

Snuzpod: (or similar co-sleeper) - made the newborn stage to much easier

Playmat: ideally with arch with hanging toys so baby can amuse him/herself while you make a cup of tea etc

Breastfeeding pillow: saved my back!

Pram organiser: got a great one from JoJo which has a magnetic seal - gives easy access to phone / wallet / travelcard

Lamaze toys: babies love 'em!

For you:

Kindle: easy to hold in one hand while breastfeeding

Leggings: you will live in them!

Slip-on shoes: so you can get them in and off easily at playgroups / Rhyme Time etc when you might be asked to remove your shoes while holding a baby

Not all essentulial but useful:
Snuzpod bedside crib
Cocoona Baby
Cheeky Wipes
Bucket with lid to soak cheeky wipes/stained clothes
Napisan
Angelcare bath support
Baby bath towels
Travel system including carseat base that takes next size up car seat
Sling (lille baby suitable from birth)
Cot top changer (until he started rolling)
Nappy bag that could fix onto buggy without taking up space in buggy basket
Buggy organiser for purse/keys/phone etc
Play mat
Lamaze toys
Bouncy seat with hanging play
Ewan the sheep
Baby gros/vests/cardigans/snow suit/hats (winter baby) - no outfits needed until much later
Muslin cloths (some extra large) bamboo
Aveeno baby bath/oilatum as both my babies had dry skin
Cotton wool.pads to clean up gunky eyes
Biodegradable nappy bags/wipes for.out and about

....and a perfect prep machine when I moved to combination feeding
MAM anti colic bottles. Never had a dummy.

....also breastfeeding tops and bras.

Coffee machine
Tumble dryer
Microwave

Ear plugs to be able to lie in or go to bed early and bank some sleep

Baby Bjorn bouncy chair, was invaluable, so was our double buggy. Also a double bed in each of their bedrooms made life much easier. If I got up, in the night, I could cuddle them and then slip off to my own bed.

Muslim squares. Lots and lots and lots of them. Very poorly reflux baby meant I went through 10-15 a day.
They also make great emergency cloth nappies

Perfect prep
Sleeping bags
Tommee tippee anti colic bottles

All fantastic