I live in a "unit" with 8 rooms with a common kitchen. Each of us were given our own set of dishes (cup, bowl, a couple different types of plates, silverware, reusable chopsticks) and we were provided with some pots and pans for the kitchen.
I hardly ever use the kitchen myself, anyway.. I eat light (fruit and yogurt) in the morning, have lunch at the school cafeteria, and I eat a combination of raw veggies and microwaveable or very simple stovetop crap (no cup noodles or top ramen, though, that stuff is terrible!) for dinner a lot of the time because I don't like cooking and cleaning up after my mess.
I will have to move out of this place after 1 year, so I'll eventually have to resupply myself with everything, but I don't mind, I'll only get what I am going to use, which might not be much.
I had to get a pillow, because the one that was provided was way too small and not of the right consistency for sleeping on, if that makes any sense. Needs to be the right combination of soft, yet firm.
I needed to get shirt hangers which I use to hang my stuff out to dry and keep it in the closet, but I got them in packs at the 100-yen store.
I might get a light blanket, the two they gave me are too thick for summer.. and maybe a new futon, the bed situation sucks. We have a bed that is like a thin set of wood planks, and it's very creaky when I roll around, and on occasion it makes my neck or back stiff. Honestly the futon straight on the floor would be much better. A second futon on top might alleviate the situation some, and I'll need an extra for when I move out anyway.
Honestly I would not recommend taking too much stuff, the little kitchen items and toiletries are cheap at Daiso and such, IMO it is worth saving the hassle of hauling a bunch of stuff.
Oh yeah you're already here in Japan. Hmm. That is a bit of a different story...
I'd say have your friends keep whatever you think you might need, and if you end up not needing something, you can toss it or give it away or whatever.