In terms of t-shirts, anything but cotton basically! Cotton holds sweat, so will make her cold. Any 'sporty' t-shirt will do, look in Millets, Go Outdoors, or middle of Lidl in running/gym weeks. Though to be honest, I just wear my thermal, I don't put a t-shirt over the top.
That list is a bit overkill - three pairs of socks, two sets of thermals, three t-shirts, one midlayer top/fleece will do fine.
Vinted is great for salopettes/ski jacket/goggles/gloves, you'll get better stuff than Lidl for less money. I kitted out DSD in pretty much brand new Superdry stuff for less than £100.
I run hot, so this might just be me, but I prefer layers rather than a big padded ski jacket. Personally, instead I would get a waterproof soft shell jacket, a padded gilet, and a fleece-type mid-layer. I would also look for one thicker and one thinner pair of gloves (both waterproof), as I get too hot sometimes in the big padded ones.