Luggage and bags:
Make sure you bring everything you are going to need, 'cause you most likely can't buy it here! There is a small general store at Silver City which carries some commonly used camping/backpacking supplies and food, but the selection is very limited and they may be out of what you need. So pack it in--pack it all in. And when you leave, pack it out--pack it all out. Leave only footprints. Take only pictures.
Clothing/Shoes/Weather Gear: It's cold here year round--in the summer months there is frequently still snow on the ground in Mineral King valley through the month of June. Although days can be nice and warm, even hot, nights, even in at the height of summer, can get down to freezing. And the Sierras are known for hosting afternoon thunderstorms during the summer months. So bring plenty of warm clothing, and rain gear. Good sturdy hiking boots. Lots of warm socks. A hat with a big brim is necessary--a hat with a big brim and a mosquito net even better. DON'T FORGET YOUR SUNGLASSES!
Toiletries and Medical Supplies: SUN SCREEN. STRONG SUN SCREEN. LOTS OF HIGH POWER SUN SCREEN. You are at high altitude here and the sun will burn you that much quicker. You'll need powerful bug repellent. Don't forget anything you may need in the way of toiletries and medical supplies--as mentioned above, you may not be able to find it at the little store in Silver City. If it's something you can't live without, and they don't have it there, you are looking at a 5 hour round trip to get it!
Photo Equipment: If you forget your camera and camera equipment, you are really gonna be sorry. This is possibly some of the most scenic territory in the world--you don't want to forget the camera!
Camping/Beach/Outdoor Gear: Make sure you have plenty of propane or whatever fuel you are using for your stove and lights, etc. Bring plenty of extra batteries. Like I said before...you may not be able to get it up here.... If you are backpacking, don't forget your water purifier.
Miscellaneous: The one thing you really, really should have--and may need to buy especially for this trip, if you are backpacking--is a bear vault or bear proof food canister. There are a number of different designs/models--the common feature being that they are food storage containers which bears can NOT open--no matter how hard they attack it.... You use it to store your food, toiletries and any items which may have a scent. This is because if the bear can smell it, he will go after it. Please read my bear warning tip! If you are out on the trails backpacking and are caught without an approved bear proof food storage container (it must be on the Park's list as an approved container) there is a fine of $150.
And Chewy is right--you will want hiking poles, an ice axe, and chicken wire.
Luggage and bags:
If you're staying at one of Silver City Resort's Rustic Cabins, bring your own mattress cover, etc. The resort provides pillows and a mattress. If you're staying in a comfy cabin or chalet, you don't need to worry.
Clothing/Shoes/Weather Gear: Okay, let's get this straight: It may be 95 degrees in Three Rivers, but it'll only be about 50 in Mineral King Valley, and going further up, it'll only be about 40 around Eagle Lake. Nights and early mornings are colder, when valley temperatures can hover just above freezing. Even if you come to Mineral King mid-summer, bring a good supplies of warm clothing. Also, always be prepared and have rain gear on hand; the Sierra Nevada creates it's own weather, and you never want to be stuck in a thunderstorm
Camping/Beach/Outdoor Gear: Outdoor gear? Pretty simple. Definitely bring hiking poles. Also, if you arrive early in the season, consider bringing an ice axe (park rangers told me I needed one to hike to Eagle Lake, but I did the hike anyway without one, and nothing really happened. Still, bring one as a precaution).
Miscellaneous: The big, big thing you'll want to bring is chicken wire to protect your car from marmots. It's very unruly and big (barely fit in our trunk) but very necessary.