Be aware that you might not be together in your ski classes all week. Even if you all start off in one group, the kids might make much faster progress than you. We first went skiing when our DC were 5y8m and 3y10m, and after two days they were going on the big lift up the mountain with the junior ski school, while we continued to fall over on the drag lift slopes. This was a huge adventure but they loved it. On the last day all the kids skiied down the hill in formation at the end of the afternoon session and showered the parents with snow by doing hockey stops. We still have the photos of DC from that holiday in frames.
In terms of kit, you will rent the actual equipment. You need a really warm waterproof jacket and decent waterproof trousers, but the latter don't have to be super-padded if you take long underwear (or leggings). Hopefully you can get use out of all of that when you return. Good gloves are essential (not wool - they will get wet), as well as a warm woolly hat and a scarf to close up any gaps in the jacket around the neck. And thick socks. Warmth becomes more important as you get better - the nursery slopes tend to be at the bottom, so perhaps only 1200m altitude, but at 2400m the wind can be very sharp and biting.
Take advice from the ski school over whether it's worth buying the full lift pass on day 1. It could be that a few single-ride clippy-tickets for the nursery lift are all you need for the first few days, and then the lift pass (which is so many Euros per day for unlimited rides) for the rest.
Honestly I wouldn't bother with pre-trip lessons. The teachers will be used to people who don't know which way round to put in skis, and dry slopes are a totally different feel to real snow.
Be aware that you will fall over, quite a lot. Skiing involves some unnatural movements, notably having to lean forward even when everything in your amygdala is telling you to lean back. Unless you are super-sporty with total control of your body movements and centre of gravity, you will not be on black or red runs after 6 days, but that's perfectly OK. (One year our instructor told us about someone who had turned up in beginners the previous week, never having put on skis, and she was on the black runs by the middle of the week. He then found out that she was a member of the French Olympic gymnastic team!)