This advice was for an exchange student going on a brief homestay during summer.
1: Bring waterproof shoes or be ready to be comfortable with soggy shoes.
2. Do not take any threadbare, scuzzy socks.
3. Try not to take scuzzy shoes.
4. Flip-flops are not worn everywhere, so don't take some with plans of having them be your primary footgear.
5. Don't worry about the slipper thing; they'll likely provide them for you.
6. Do worry about which slippers are for where. There are outside plastic slippers, (sometimes) kitchen slippers, (usually) indoor slippers and (always) toilet/WC slippers. They are not worn outside of their designated areas, so pay attention when coming out of the toilet! Do not wear slippers or anything other than socks on tatami mats. If you mess up, though, it's OK because you're a gaijin.
7. If you go to shrines or temples, you will likely have to remove your shoes at some point. Some places have lockers or shelves for your shoes; some have slippers; and some have nothing but plastic bags to put your shoes in. Don't be surprised by this and imitate what others do.
8. Before you enter the grounds of a shrine or temple, you should ritually wash your hands and rinse your mouth. There will be a place for you to do this called a chōzu. The etiquette for this varies. Take the water in the dipper and use it. Be sure that your wash water does not fall in the clean water area. Although not essential, it's nice to take another half dipper of water and rinse the dipper by tilting it up so that the water washes the handle. Again, imitate others. The details are important, though, as you don't want to embarrass your homestay nor gross people out.
9. Most shrines and temples have osaisen-bako or money boxes into which you throw some change before ringing the bell (kashiwade) and clapping, then praying for whatever it is you're praying for. Again, imitate. Don't feel you need to offer much; 5 or 10 yen is a common amount.
10. Omamori, or charms from shrines and temples, make for interesting, lightweight and usually small, thin and hard to break presents. Common charms are: protection from accidents, protection from car accidents (left in the car), passing a big test, love, pregnancy, longevity, protection from illness, success in money matters, perseverance, etc., etc. and usually cost from 400-800Y.