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

[bradleybecky]

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Perfect Prep machine
I got given a towel with a hood that also clips around you like an apron. It stops you from getting soaked when giving baby a bath. Something like this

Bibs! ! Wasn't listed on the list to take to hospital, we got everything else, ended up spending a few days changing her constantly after every feed, hubby taking her stuff home from hospital and washing and drying every night, when eventually someone said came in to our room at hospital and said " why has she not got s bib",,,,doh,,,cue hubbys mad dash to moghercare. 😳

A bedside crib
Baby refused Moses basket

Barely bought anything but got a great stretchy sling.

Wish I'd had a couple sleeper cot and an angel care monitor. I was so paranoid about him stopping breathing I used to wake him up to check he was alive

Bouncy chair. Used it all the time.

Ewan the dream sheep. Second would be sleepyhead

Another vote for giant muslin squares- swaddle, breastfeeding cover (if you want to cover), sunshade, emergency play mat, clean up cloth, bib and tie a corner in it and it makes a decent chew toy!

Other than that washable wipes so much better then wet wipes for clearing up nappy explosions.

Dh came in one day when ds was about a week old with a changing table. I grumbled at the time about the ridiculous waste of money. Now I wouldn't be without it at all especially now that ds is a toddler. I only really realise how much I appreciate it when I'm visiting a friend without one & end up trying to have to wrestle ds in a bid to stop him escaping while I'm changing him.
Also they save your back during the newborn days when it seems like the nappies are never ending.

Ewan the sheep
Muslins ( my friend just uses loo roll!!!)
Sleepyhead
Perfect prep

I'm going against the grain and saying that I didn't find muslins, Ewan or a sling useful.

Best Buy here was a sleepyhead, and Gro bag once dd was big enough. And for me good comfortable boots and a good coat for the miles I walked with the Pram.

Cheeky wipes. Still going strong and DC2 is two.
Sling and sleepyhead next, never really used muslins as mine weren't pukers.

Gro bags - the own brand ones from Mothercare or the supermarket were fine, no need to spend all that money on branded ones.

Perfect prep machine
Lots of muslins
Swinging chair

Not strictly a baby item but I was given some covers that you put on top of a mug of tea/coffee that keeps it hot for longer, not sure what they're called but I think they were from Lakeland, perfect when you make a tea but then baby needs changing/feeding etc and you can't drink it straight away.

We bought a Grobag with the holes in the crotch area for a 3 point harness. It meant we could get home from work on a Friday, have supper, bath DS1 and put him in his carseat & set off for my ILs for the weekend, then transfer him asleep to the travel cot on arrival without any faff. It is a horrible drive to their house, but going in the evening meant a clear weekend without having to battle through rush hour or daytime traffic. The Grobag was much more successful than babygrows/PJs & blankets - he always woke during the car-house transfer then.

Fisher price infant to toddler rocker (I had twins and I could feed them both at the same time in these).
Muslins
Enough bottles / teats to wash them up once a day if FF

Perfect prep machine

Never owned a muslin, not really sure what I'd have done with them.

This is a slight diversion but when my DC1 was born in 1980 I used my whole
Maternity grant of £90 to buy a sewing machine from John Lewis. Best £90 ever, it's still going strong 36 years later and I'm about to make said DS some curtains for his DD's bedroom.

My Ergo baby carrier. Used from birth until about the age of 3.5, I have got rid of everything else baby related as soon as no longer needed by the DCs, but I hope to one day use my Ergo with my grandkids (eldest child is 6...!)

Large Muslins from Aden and Anais

Sling
Sleepyhead
Sleepsuits with built in mitts

Perfect prep machine, 100%

A breast pump because it meant I could go out and leave DH in charge. Felt like my passport to freedom. Interestingly, I barely used it for my other DCs, probably because by then I'd got used to going out and taking a child or two with me.

I've had either 2 babies, 1 baby and 1 small child or 2 small children at most times.

So for me, it would be things that can grow. Prams that can convert for 2 children etc. Reusable nappies that will cover the bums of more than one child. Neutral newborn clothing that can be passed down. The most expensive car seats you can get that will grow with your child instead of having to replace all the time.

A cot top changer (not sure if mothercare still do them as cheaply). We had no room for a change table and this was the next best thing.
A bath frame, no idea what they are actually called, it was a basic frame with a terry towelling cover that you use for newborns in a normal sized bath.

Moses basket, ds was in it until 3 months and so good to put him in when I was showering etc!

Gro swaddle when new born then gro bags, although not branded ones as tk maxx do loads that are much cheaper. Saved me worrying about blankets and suffocation!