Ski gear can very quickly get expensive, so your first option should be to see what you can buy or borrow from any other families that also ski. Failing that, second-hand from Vinted, ebay etc. is fine - there are thousands of wardrobes and cupboards full of ski stuff that has only ever been worn once or twice before the kids grew out of it!
Jackets and salopettes are the way to go (for adults too) rather than snowsuits, which are a pain when you need to visit the toilet - which you will need to do at least twice during any ski day.
If you are going to buy new look at Decathlon, Dare2Be or Trespass, or even the ski clothing sold by Aldi every year in around October/November. All are decent quality, particularly Decathlon, and good value for money. Obviously you'll need your own ski underwear, so again, look at Decathlon or Aldi for reasonable, affordable stuff. On top of that you'll need fleece layers, especially as you are going in January. Everyone needs two pairs of gloves - mittens for the children are better and warmer than gloves - and 3 pairs of ski socks. Get proper ski socks - stay well away from tube socks with snowmen or reindeer on them as these will bunch up in the boots and cause blisters. Also get a Buff and a knitted hat. Once you get bitten by the ski bug (and once the kids stop growing) you can splash out on the really expensive brands and pay £800 or more for a jacket, but until then, the basic stuff from Decathlon etc. is fine.
Avoid any "fashion" brands - these produce clothes for posing around the village and bars in rather than ski clothing that will keep you warm (and safe) on the mountain. And don't buy anything white. The Sunday Times and other papers seem to produce annual "ski fashion" features that somehow manage to highlight the sort of clothes that nobody who skis seriously would be seen dead in, but which are fine for sitting outside a cafe with an Aperol Spritzer and a little lapdog that matches the fur collar on the utterly impractical ski suit.
The ski rental shop will provide helmets, which are compulsory for children in most resorts and ski schools.