Luggage and bags:
With the 93 mile Wonderland Trail encircling Mount Rainier, this is one place to bring your backpack but there are many shorter hikes that a day pack will suffice for.
Clothing/Shoes/Weather Gear: Sturdy hiking boots and warm cushioned socks will keep your feet happy. Dress in synthetic layers to keep yourself warm and adaptable to the ever changing weather around The Mountain. A warm hat sounds funny when packing for a summer trip but in the mountains you'll be glad you have it, especially if camping. Rain gear is an unfortunate necessity in a park that gets its fair share of the wet stuff. Hey, that's what makes it so green and you appreciate Rainier even more when it does come out to play.
Toiletries and Medical Supplies: Sun block is important to wear when this close to the sun. Yes, the sun does shine and when it does and it reflects off all the sun and ice, it's a killer.
Photo Equipment: Bring your wide angle. This is one HUGE mountain and you may not be able to get it and a reflection into normal range lenses. A zoom is great for your wildlife shots and bring a tripod for early morning/evening light and for getting those cute couple shots.
Camping/Beach/Outdoor Gear: Rainier has some of the nicest and most reasonably priced campgrounds in the National Park system so by all means bring a good tent, sleeping bags, mats and a cooker. You'll save money and see a lot more of the nature you came to experience in the first place.
Miscellaneous: It's easier to wake up early if you have someone to share it with. Thanks, D.
Clothing/Shoes/Weather Gear: The mountain makes its own weather and the Paradise side is ranier than the Sunrise side, so be prepared for anything. A summer day can begin cool and cloudy and warm up quickly. Rain is always possible, so dress in layers and bring raingear.