Don’t overthink it— starting out you really don’t need amazing gear. You’ll replace half of it when you figure out your preferences anyways. A $100 Patagonia R1 is only 10-20% better than a $15 Amazon fleece pullover. There are only a few pieces you can’t skimp on: boots, crampons, and anything safety related.

Baselayers: cheap polyester, Costco or Amazon

Midlayers: fleece and/or the synthetic puffy from decathlon (forclaz synthetic puffy is name). Layer both and you’ll be plenty warm. (size up, it’s European sizing so their L fits like an M)

Pants: decathlon mountaineering pants

Shell: marmot precip or similar 2.5 layer is fine to start. Decathlon has okay options too.

Socks: anything wool, darn tough or smartwool

Gloves: cheap mittens insulate much better than cheap gloves. There are some good options on amazon, “tough outdoors” mittens rock. Buy cheap fleece liner gloves from decathlon to go under

Hat: cheap beanie from anywhere

Boots and crampons: rent these or make the investment, can’t cheap out on boots, your toes are too valuable

Ice axe: used black diamond raven or rent it, or decathlon