I bought a couple books about hiking on Mount Rainier, and neither gave me any good information about what equipment I would likely need to hike to Camp Muir and stay overnight. So I have been searching the net.
On the national park service website at http://www.nps.gov/mora/climb/climb.htm, they listed a bunch of equipment. But some of it I think is for a climb all the way to the summit. I doubt I need prussik slings, ascenders, ice screws, or 40 meters of rope.
RMI’s website had a good list also at http://rmiguides.com/rainier/muir_sem_equipment.html

I know I will need a better sleeping bag than the cheap Walmart bought sleeping bags that we currently use for camping. For reading the lists, it appears that I will want a sleeping bag good down to 10 or 20 degrees. Some brands I have seen recommended have been Mountain Hardwear, Marmot, and North Face. Other choices are down, and synthetic. I am leaning to synthetic as it seems easier to maintain, and will work better if it gets wet. It also seems to be a little cheaper. I saw a Marmot bag on sale for $69 at Dick’s Sporting Goods that was good down to 20 degrees. I am in no hurry though as I wont need the bag til next year.

I will also want a parka. I can actually use a park here. The winter temperatures here in Rochester, NY can get down to near zero or even sub-zero. I know one year it was -8 degrees outside and windy while I was clearing snow off from my driveway.

I have a Kelty external frame backpack which will should work for the trip. But I may look at an internal frame pack anyway,

I have done a lot of geocaching, so I already have stuff like compass (military grade with tritium markings), knife (Swiss Army), headlamp (Princeton Tec Vortec), and of course a GPS (Magellan Map 330).

I have done some skiing so I have ski goggles, and ski gloves, hat.

And from camping, I already have a nice lightweight stove, sleeping pad, two person tent and some other stuff like that.

We can always rent some equipment as well.

I recently bought the Montrail Torre GTX hiking boots which I am working on getting broken in. So those should be more than good enough.

I am not sure if I will need crampons to go to Camp Muir in June. Both web sites recommend 10 or 12 point crampons, but those might be more for going to the summit. Some other things I have read suggested they may or may not be needed.

I will need to figure out what other clothing I will need. I know people do day hikes to Camp Muir without a lot of gear. But we are planning on staying over night, and I am sure the temps will drop. I porbably don’t want to wear jeans as all the cotton. Or maybe I wear jeans, and then wear something over them. I don’t know. I have almost a year to figure it all out.