How can I see my best current store-wide rankings for each book, store, or country?

Open the Rankings screen, ensure that the drop-downs are set to "Store-wide", "Day of", today's date, and "Book" (or "Store" or "Country").  If you want to see your rankings for a different date, just change the date.  If you want to see all categorized (non store-wide) lists, choose "Categorized" instead of "Store-wide" (you can also choose a specific category -- note that categories are per-store, so if you choose a particular category, you are automatically filtering to a single store).

If you want to see rankings for a single book, store, or country, the filtering drop-downs at the top of the screen can be used.