Are you going to be skiing or snowboarding?
In terms of clothes it doesn't make a difference which but if you are going to snowboard I would strongly recommend learning before you go, it will make the holiday that bit more enjoyable.
I would suggest 2 coats and 2 pairs of salopettes. You dont want to be heading out on the mountain with anything that is wet/damp and if your gear hasn't dried over night for what ever reason you want to be covered.
Most of your first lot of gear you can get away with going on the cheaper end of whatever you find. I would avoid shops like Ellis Brigham etc and aim for things sold in Tresspass or Dare2Be which are all perfectly acceptable.
Sunglasses - I would strongly recommend goggles, the extra coverage alone makes them far superior to glasses.
Gloves - 2 pairs.
Get a balaclava or buff protecting your face from the cold is going to make staying warm easier. With a buff you can put it on and then pull the back part back over to rest on the top of your head, this will also cover your ears and be easier for it to stay up at the front as well to cover your mouth/nose as required.
Helmet - don't go without one! or make sure you rent one, no one should ride without one, and anyone who does is a fool.
If you really want to be sure your jackets/salopettes will protect you, you can get some wash in sno seal to waterproof them.
All in I reckon you will get a good selection of everything that will be more then good enough for £300-£400 max.
TL/DR
2 Jackets
2 pairs of Salopettes
1 buff/balaclava
2 Pairs of gloves
Goggles not sunglasses
Helmet
Snoseal wash in waterproofing