generally, I think "meow" is usually used as a transcription of what the cat, or kitten, actually says. "Mew" is the verb used to describe what it does - so a cat mews but it says "meow".
But the noun... "the cat's meow" is a common phrase, meaning much the same as "the cat's pyjamas" or "the cat's whiskers" - to mean "something great"
http://www.urbandictionary.com/define.php?term=the+cat%27s+meow
But when it's used literally about a cat, I think meow or mew are probably equally used. To get round it, you could say "the cat's mewing" (that's using mewing as a noun, rather than short for "the cat is mewing").
"Miaow" is I think a slightly old-fashioned way of spelling meow. You could argue that because it has more vowels in it, it represents a slightly longer and louder noise than "meow" and so as mamyalynne says it would sound better used about a cat than a kitten.
Happy new year in the far north!