I have a 3 month old and a toddler. For the most recent baby I bought 10 vests and 10 babygrows, but she grew out of the 0-3 by week 8 😆 you only realistically need 2 or 3 blankets (car, upstairs, downstairs). You need about 4 cot blankets in case baby is a sicky baby, and a water proof cover for the mattress on each cot. I chose to have a cot in the sitting room and then the cot upstairs. As you will be having a baby in late spring into summer you dont need to bother with snow suits, hats etc. Muslins are also a must have, about 20.
A decent monitor is great if you plan to leave the room where baby is. I leave DD sleeping in the sitting room and pop in to do the wash up for 15 mins and bring the monitor. Its obviously good too when they move upstairs for naps when older.
I bought morrisons sleeping bags (2 bags, 2 tog, then 2 lighter ones for summer), 0-6. They dont always fit in them when newborn. Some people like gro bags, or snuggle bags, but they are expensive and baby doesnt always like being swaddled, so maybe just wait and see what baby likes first.
A playmay is good, as is a bouncer as you can bring them with you in the bouncer. One odd thing I use is a baby nail file. Their nails are talons, and I cut my firsg baby with the baby nail scissors. Nightmare. If you plan to formula feed one of those formula storage holders with divided sections is brilliant, as is two 500ml flasks for water.
After that, there really isnt much they need. Babies are pretty basic tbh. Most stuff is just trying to convince parents to part with their money.