My advice would be to choose a resort with the quickest access to the slopes you can afford. Long walks or ski buses with kids in ski boots and (you) carrying all their skis are not fun in my experience.
We use Val Cenis. It is much cheaper than many French resorts and we save a fortune on half term flight prices by driving. And get one and a half extra days skiing. Six day lift passes are just 165 euros. Our accommodation 20 metres from the snow costs about 1300 euros, there are usually apartments from about 750 euros but they involve longer walks so aren’t good for kids.
Book ski hire online for discounts. Last winter Decathlon did vouchers in store giving an extra discount off their Skimium hire rates online.
February half term week cost us about £3500 for a family of 5 all in, including ski school and ski hire for the kids, some private lessons, food, tolls, fuel, hotels en route, the lot. We tend to eat in. Smaller resorts in the valley, like Aussois or La Norma would be adequate for a first trip and probably even cheaper.