Babies don't need much beyond food, warmth and cuddles. In my area you'd be classed as a "Young Parent" so get to your nearest Children's Centre and see about some extra support, even if it's just an introduction to other mums who are or have been in a similar position.
I would get a pack of 5 vests and 2 packs of 3 babygrows in new born size, just cheap ones from the local supermarket. Then, you can go shopping for nice clothes when you know how big your baby is. Mine was 6 lb 3 oz and my mum had to buy Tiny Baby sized stuff on her way to visit for the first time 
You might like to get a nice outfit for both of you to come home in.
A couple of cardigans, a warm hat and some nice blankets will be plenty for in the car or buggy - you don't want a snow suit in the car as you won't be able to tighten the straps enough for safety, but if you plan to walk a lot it'll be useful.
Don't forget muslins and bandana bibs in case you get a sicky or dribbly one
The shops will be open after you've given birth, and shopping centres are nice and flat and people don't mind too much if you amble slowly due to having just given birth. M+S is the best place to find older ladies who will tell you what a beautiful baby you have, how well you're doing and generally boost you confidence in the blur of the first few months!
Congratulations 