Winter tires are amazing; after you've had a set there is no going back. The grip they give in poor weather is incredible. They're also much better on cold, damp tarmac, so they are definately not 'snow tyres.' Driving a car with summer tyres in the winter is frankly terrifying in comparison. Don't let anyone tell you that 'just drive slower in the snow,' or 'its never that bad in the UK.' They really are good.
Narrower tyres are theoretically better, but I'd just get a set in the same size as your standard tyres. I've got a set of 16" wheels from a GT Sport with my winter tyres on, but that's more because I already had the tyres from my Audi A4. You can also fit standard snow chains on the 16" wheels, rather than posh ones.