For an added bit of fun (particularly if you're a language student, as opposed to just wanting to get stuff done), have a look at the Character Palette.
In that same Input Menu preference (System Preferences --> International --> Input Menu), turn Character Palette on.
Now select Show Character Palette from the input menu. The floating window that appears will let you browse the characters available in any font, in any language, but the Japanese section is particularly nice (select "Japanese" from the "View" popup menu at the top).
It allows you to view essentially all Kanji sorted by radical/stroke count or name, it lists all On and Kun readings of the selected character, shows you alternate variants of the character, and best of all gives you a full preview of what that character looks like in every font that includes it (you may have to expand the little "Font Variation" triangle at the bottom).
That last one is incredibly handy for previewing decorative fonts, even more so because it also lists Chinese fonts (many of which also seem to have a basic kana set), so for most characters it gives you a hint at the much wider variety of fonts available than if you were just looking at Japanese.