How do I know whether I should use flat-leaf or curly-leaf parsley? I'm interested mostly in their uses as ingredients, but guidance on usage as garnishes is also welcome.
Flat-leaf (also called Italian Parsley) and curly parsley can be used interchangeably but most chefs prefer flat leaf as it usually has a more distinct taste. That is going to be up to you and your preference.
Curly parsley provides a more unique and visually interesting look when you're talking about garnishes but putting a sprig of parsley on a plate is what would be called a "non-functional" garnish. Aside from adding a bit of green it serves no purpose as very few people I know will pop it in their mouth and eat it. You're better to sprinkle with chopped parsley or herbs that can help enhance/accent the flavor.
Curly parsley is also visually appealing used in a parsley salad due again to the ruffled edges.
I usually use flat-leaf if available, then curly if flat-leaf isn't available. Under no circumstances (except if you just need a touch of green dust) do I recommend using dried parsley. Clippings from the underside of yor lawn-mower probably have more flavor. Same goes for dried chives.