In my opinion, once you get to 6-9 and beyond you can pretty much trust those sizes, however, smaller than than and shops are SO different. For example in Next I believe their Newborn is only up to 7.5lb (where we got Ella's first outfit which fit her ONE time) and yet Asda and John Lewis are something like 9.9lb or above. So I would check the labels and buy newborn stuff which has a larger weight boundary. Also depends how big your baby is... Ella was 7lb11oz and most of the shops newborn fit for a month or so then 0-3 still was huge on her after that - but to be honest when baby clothes are a bit too big at that stage they just look so cute! Haha but that's my opinion!
Also, depends a bit on length. Ella was always petite and still is now but she has avery long torso and shorty legs like me, so being she's only 9 1/2 months old, she's almost outgrown 9-12 sleepsuits and vests, anything all in one, but dresses and tops in 9-12 fit fine, and trousers she is still in 6-9 because of her legs! So it does depend on your baby. Either way, you will need a lot more 0-3 things anyway because that covers 3 months. But get a few newborn bits, comfy things like babygrows and sleepsuits cus that's cosiest for a new baby anyway.
Sorry that was a tad rambly hehe xxx