we didn't go to any baby shows. You are a captive market there and you can't pricecheck and in my opinion you'll end up buying loads of stuff you won't ever need/use.
things we bought for DS, not all were essential but this might help with where to start!
moses basket with a rocking stand - which was great for taking to my parents for a weekend when he was 6 weeks, however he outgrew it by 11 weeks so we then bought a mothercare glider crib, which he could easily have stayed in till 6 months or more, but we ended up moving him into his own room/into his cotbed at 5 months so we could get some sleep as he snores! i would add that the rocking motion of the moses stand and the rocking of the glider crib were a godsend for getting him off to sleep.
merino kids sleeping bags - they are one size, which fits them from birth to approx 2, and you don't need a summer one and a winter one, as they are made from merino they are breathable and stop a baby overheating, but machine washable and can go in a tumble drier. So whilst they are pricy at £50 each, its actually lot cheaper than various summer/winter ones in different sizes from other ranges. Our DS would not stay under the various blankets and sheets we wasted money on, and a cold baby= a waking up baby....we would never bother with sheets etc again, just a long sleeved vest under a sleeping bag and he slept so well - he was doing 8 hours overnight by 6 weeks :)
buggy - we bought baby jogger city select, with a buggy seat, a spare seat and a kit to convert the spare seat to a carry cot. It can have 2 children on it, so will not need to spend anymore for DC2. It can also fit a buggy board if have 3 close in age.
car seat - maxi cosi cabrio fix and an easybase for the car as we don't have isofix
closer to nature bibs - have a lovely soft thick band, stops milk dribbling and DS never got any rashes
lots and lots of muslin squares - ASDA direct is great for cheap bits like this but not sure if they still stock as much as they used to.
baby bath - saved my back as could rest it across our bath, rather than having to lean in.
changing mat - get 2 - one for upstairs one for downstairs
in our case, lots of old towels to lay down wherever we fed DS as he had reflux and in the early days he would soak through our duvet cover/duvet/sheet/mattress!!!! towels limited how far/deep his sick would spread....
infacacol - a lifesaver - get lots of bottles
gripe water for when slightly older - i think 1 or 2 months old (we gave gripe water with cooled boiled water, so although he was BF, we did need a steriliser and bottles, got a cheap microwave tommee tippee steriliser, and some tommee tippee closer to nature bottles, and never had any feeding confusion from DS and he has BF to 15 months.)
An in ear thermometer - this really is important as you need to be able to get an accurate/quick temperature.
at least 7 vests and babygrows for each age group. We got ones with built in scratch mits in the younger ages, and all were cheap ones from the supermarkets, as there is no point spending lots on these as they will poo on them, throw up on them, and then grow out of them very quickly!
nail clippers as they will need cutting at least once a week.
a baby monitor with room temperature on it - we now have a video one and if you can afford it, it is well worth it for when they become mobile, as DS often makes crying sounds when we put him in his cot, but we tell him through the monitor to lie down, and he does, but the noises are the same for a short while, and if we couldn't see he was lay down, we would probably end up going in thinking he was upset, when he isn't, its just the noises he does before he goes to sleep.
cotton wool for the early days for cleaning eyes and around the cord. we used babywipes on his bum from birth, never had any issues, but we are using the pampers sensitive ones, which are super gentle.
Dentinox shampoo - great for getting rid of cradle cap.
in the early days, the only toy we had for him was a hugnry caterpiller one, which kiddicare are still selling for about £17 - and he still plays with it now so a good buy, it is lightweight and has lots of textures and he wouldn't go anywhere without it from very early on.
a playmat with arches over it and various toys suspended from the arches. We got a baby einstein one as it has an electronic box on it that lights up and plays music - which DS loved.
a vibrating bouncer chair - helped to get him to sleep in the day and he loved being able to see a bit more of the world around him rather than just being stuck on his playmat.
when about 4 months, a jumperoo is one of the best things i can recommend if you have budget/space for fun but not essential things!! DS has used it up until now, but he is about the max weight for it now so we packed it away this weekend.
highly recommend the mam teethers - they come with clips to attach to their clothes so whenever they drop them, the teethers are still in reach :)
for yourselves, get lansinoh ointment and their breastpads are very good too - have two sticky labels on which keeps them in place better than other brands i tried and they are very soft.
i also got a breast pump as planned to express so DP could do the occasional feed, although in the end this rarely happened as i found it a lot of faff and so didn't bother with it that much.
if i think of anything else i will post again!