We learned to ski in Rauris in Austria aged 38, 6, and 8. Rauris is a tiny resort, so not intimidating for beginners, and impossible to get lost. The second time we went, we opted to stay in this slope side accommodation, which was gorgeous and offered direct access to the Adventure Rauris ski school meet point (we've used them and they're excellent).
https://www.booking.com/Share-nQjGuZ
Rauris is around 90 minutes by train or car from Salzburg.
We opted to pull ours out of school the week before the February half term, and the savings on flights and accommodation more than covered the cost of the the fine. We did notice an increase in people towards the end of the week, so agree that February half term will be busy.
Were skied February, Christmas, and Easter and Easter is by far our favourite. Longer days, lighter nights, warmer weather.
Rauris would be no good at Easter, but one of the high French resorts would be absolutely fine. We love Les Arcs. It's a huge ski area, but would be a fabulous place to learn, with long, gentle blues. If you stayed in 1950, you'd get the full family friendly, ski in/out experience as you can literally ski through the village as it's car free. This guys YT demonstrates it well. I'd recommend Evolution 2. Lessons in English and a maximum of 8 per group.
I think it's about 2.5 hours from Geneva, but have only driven it (10 hours from Calais) so can't comment with any authority. Next April we're getting the train there from the UK, so are looking forward to relaxing on that.
To answer your questions. We always book it independently.
First we book accommodation. Go for Saturday to Saturday as ski school generally runs Sunday to Friday.
Then we book flights as soon as they open, or if driving/train, book Le Shuttle/Eurostar around the same time as accommodation.
Next we book ski school. They usually take bookings from the September before the season starts.
Then lift passes. They usually go on sale around the November before the season starts and there are often early bird discounts if you can book then.
Then ski hire. Though in Rauris we booked it with the ski school at the same time as lessons and got the DCs as a lesson + hire bundle.
Then the rest sort of falls into place after that.