It all depends on the time of year. And the weather that particular day. And about a million other factors. If you go in July or August, and the forecast is good, then you might actually need a pretty minimal setup. But if the wind picks up, or a front moves through, then you need to be dressed as if it were January. There's just no telling.
I last climbed Rainier this past July (winds of 60 to 70 mph drove us back at 14,000 feet). My basic setup for that trip, as for several others there, went like this: Parka and pants made from some sort of waterproof-breathable material. In July, I was packing a Mountain Hardwear Gore-Tex XCR jacketthe Ethereal FTX ($440; www.mountainhardwear.com)and light L.L. Bean Gore-Tex pants, although these actually were a prototype I was trying that Bean never produced. Arc'Teryx's Beta LT Pants ($235; www.arcteryx.com) are similar.
A set of light long underwearPatagonia's Lightweight Capilene Zip-T ($38; www.patagonia.com) and a pair of matching Silkweight Tights ($32). I THOUGHT I had packed a set of Marmot mid-weight bottoms as well, but mistakenly packed another top. Dope slap when it got cold and windy, but the Silkweights felt remarkably warm under the Bean pants.
A mid-weight top, something along the lines of REI's Midweight MTS Zip T ($35; www.rei.com).
A mid-weight fleece jacket: Patagonia's R3 Radiant ($138) did the trick for me.
Cloudveil's Run Don't Walk Vest ($75; www.cloudveil.com), for just a little extra torso warmth.
An assortment of hats and gloves.
Shorts and T-shirt for warmth below 10,000 feet (though we didn't have much of that, even in July).
Salomon's new Super Mountain Expert boots ($390; www.salomonoutdoor.com), which I must add were great.
So, not a ton, but enough to layer up pretty thoroughly. An extremely nice add-on is some sort of light down sweater or jacket; for this, Feathered Friends' Volant jacket ($235; www.featheredfriends.com) is the ideal Rainier "comfort" and just-in-case piece.
This list can be mixed and matched in several ways. The keys: Some warmth, some windproofness, and some waterproofness. When it comes to Rainier, though, start by setting your base scenario at windy and temps of about ten degrees.