Best/essential purchases:
Receiving blankets (think in the UK these are muslins?)... use them as burp cloths, use them for swaddling, use them for blankets
Blankets
Plastic bibs.. when baby starts to have foods, esp feeding themselves, the Bumkins bibs are fabulous. Like $5.49 for one when they're on sale here so very reasonably priced, waterproof, don't need to wash it, and they have a pocket to catch food baby drops
Clothes in a variety of sizes. (I didn't buy anything smaller than 0-3 months but thank goodness my friend who has a son bought me some preemie onesies with one of my gifts and some newborn clothes, my LO was swimming in newborn clothes at 6lbs 1oz- went home 5lbs 15oz)
Baby monitors... INVEST IN GOOD ONES
I hate the static I get with mine, if I could go back, I would have splurged on better ones. Newborns especially can be quiet when they cry, and it's nice to be able to hear what they're up to once they get older, sometimes they just wake up and play around.. sometimes they don't go to sleep and they play around, and you don't have to sit in silence nearby w/ monitors you can go downstairs and do your washing or watch TV etc.
Bouncy chair... if you can, one with a removable toy bar, and one with a vibrating setting is nice to soothe them
Mobile
Fisher Price Ocean Wonders Aquarium soother - my baby loved this, I let her have it the first 5 months. Then she learned how to turn it on and off on her own and I had to take it away because it kept her up.
Onesies, sleepers, booties, a little sweater, hats, mitts.. don't go too nuts but have the basics!
Baby care kit- mine included a brush, comb, toothbrush, nail clippers, nasal aspirator, syringe for medicine, nail files
Thermometer- I have a Braun digital read that goes in the ear. It's fast and easy to read, it was like $75 and I hope I don't have to use it that often, but TBH I prefer it even to take my own temperature, and when you need to take baby's temp, it's a pain to do it orally, and I'd be afraid to use a rectal thermometer
FORMULA--> not available in the UK as far as I know, but in the USA & Canada it is... don't bother with the powder- the concentrate is so much easier- no measuring, it's more sterile, and it works out cheaper for us, even though a case of it is $35-$45 and a tin of the powder is $20 something.
Playpen/playard/pack n'play- most come with a "bassinet" height setting. It is killing 2 birds with one stone if you want a portable bed and a bassinet.. no, you don't get the fancy bassinet/moses basket but it's smaller than a full size crib, portable, etc. When you have it at bassinet height, you can use it as a change station as well. Some actually come with diaper/wipes spots.
Baby Motrin... I prefer this to baby Tylenol or baby Advil
Change pad/station w/ belt... I don't have one of these but I need to get one, they're only $30 anyway. When they are a little older they are a devil to keep still for a change.. tricky to not get poo/diaper cream on you or the changing surface... or me, I end up with a barebummed baby crawling away from me before a new diaper is on
Worst/unnecessary purchases:
Soothers- (Dummies) I bought a couple packs and was given tons with gifts, and my baby wouldn't take them. One pack of 2 would suffice.
Any outfits for the first couple of months- easier to just put them in sleepers etc.
Room thermometer- in the UK loads of people seem to have them? Here we don't use them and manage just fine
Rule of thumb for dressing baby = one layer more than you. It's not hard to dress baby properly for sleep either IMO, and when they are young they get up often enough that you can check and stay on top of that.. when they are older they squirm out of blankets etc
Special baby detergent... unless your baby has sensitive skin, they can use what the rest of the family uses. I really like the Baby OxyClean stain spray, I buy baby because it is the same price as the regular (I have never thrown an outfit out due to stains and I have a 10 month old because of this stuff! and I am NOTORIOUS for forgetting bibs at bottle time
)
Diaper Genie, diaper disposal systems... regular trash can will do, TBH if your child poos it STINKS and you'll probably want it out of the house ASAP anyway
not sitting around in a pail in the nursery or bathroom etc.
I'll think of more I am sure.