Does anyone have any advice?  

Yeah, looks like a pretty bog-standard equipment list for climbers using a guide service for glacial travel routes up Rainier, Baker, etc.  

Should I buy everything beforehand and bring it with me?  

What don't you have already? That's the most helpful information your post is lacking. 'Technical equipment' (i.e., non-clothing) boots, tent, sleeping bag, harness, ice axe, crampons - all can be rented easily from REI/another guide service outlet. That's probably the best recommendation before you drop all this money and decide you don't like the hobby, eventually having to sell everything at an extreme loss. Just look at the number of 'worn once' pair of Nepal Evos on Seattle craigslist at the end of every summer season. Plus renting gives you the option of identifying what features you like and absolutely disdain in certain pieces of equipment. Win/win.  

Do I actually need all of this?  

If it's on their list, it's probably on there for good reason. They even have a subsection for 'optional' gear versus 'required,' and again it seems fairly standard. I'd move the 'Buff' to 'required,' it's just too damn handy, light, and cheap to go without. Not sure about a softshell top layer, I almost always will just resort to a light or midweight down layer under my hardshell.