Your Company Housing apartment will not have linen or toiletries provided at all. You will need to bring your own sheets (twin, not XL, and your mattress will be thin, you don't need anything close to deep pockets) and towels.
There are lockers and changing rooms at every work location, and they should be near Costuming. You will see all of this when you take your property tour at your location. Many CPs do wear costumes to work. This saves time in case something happens to the bus, or you're just running late. This way, you know you don't have to waste time with Costuming, and you can just jump into work. You'll learn what's best for you.
Don't worry about not being packed. 16 days is a lifetime. I packed the day before and I had 2 cars full of stuff. When I moved into my new apartment, I had 3 car loads, but I only moved about 2 miles away. We packed the night before we moved and didn't sleep at all.
You'll be okay!