A 1 BR Comes with basic kitchen supplies including paper towels, dishwashing liquid and powder dishwasher soap. If you plan on cooking, you may want to bring along a non-stick skillet, since the ones in the rooms tend to stick.
You will get a small box of tide for the washing machine, so you should bring more laundry supplies if you plan on washing your clothes (You can pick this up at the store in the resort, or the laundry room, but it tends to be $$).
You will receive linens for the bed, sofa bed and portacrib (which will be in the room).
You will receive around 2 bars of bath soap and 2 bars of hand soap and shampoos (same stuff you get in the regular WDW rooms). If you are there for T&T or a cleaning day, they will replace it.
The room will have a vacuum, iron and ironing board.
I usually bring along some Clorox Wipes, Lysol, my own laundry supplies and my own soap (Lever 2000 - wouldn't want to miss any of my 2000 body parts

).
I'm sure I probably left something out...
BTW: Search around if you're looking for rentals. There are some great people out there. Make sure you are comfortable with the person you're dealing with.