Having been skiing in the Alps most seasons for nigh on 30 years, I have very rarely needed a fully waterproof jacket. In the UK, where often the snow can be wet and miserable, get full waterproofs.
I ski in a thin long-sleeved base layer, a mid-weight fleece and a thin, very breathable and very windproof top. It is not waterproof but will keep out all but the wettest snow showers. I carry a small mid-weight fleece for if it gets colder but have rarely needed it. I find breathability a more important factor than out-and-out waterproofing. My mid-layer fleece cost less than £10 from Aldi.
A good hat, gloves and – for me anyway – a neck gaiter, are essential.
That said you will end up on your bum a lot, so do get some decent, hard-wearing and waterproof trousers. Salopettes are good because they give you slighter better coverage around the lower back and can't fall down. Ease of movement is key but the baggy question is one of style IMO.
To put this in context, it used to be my job to convince people to buy super-expensive ski and snowboard gear. For the base layers and fleeces the deep-discounting supermarkets are a great bet. The money you save can be spent on a nice looking pair of goggles 😀