Loaded question for sure, but I'll take a whack at it.
Different lines for different applications, I've got reels lined up with all three, and several with copolymer as well.
Just a general idea of what works for me:
Mono: Floats well, but least sensitive line, also least expensive, I'll use it for:
Topwaters, good for cranking and jerkbaits too
Fluoro: Sensitive, tough, it's dense and will sink so it's not a good topwater line, also it's expensive:
Draggin' jigs or plastics
Braid: Maybe the most versatile line. It floats, it's the strongest, the most sensitive, somewhat expensive, but it will last years on a reel without memory issues:
Heavy topwaters, frogs, buzzbait, punchin', sometimes spinnerbaits, chatterbaits, and cranking. Many people (just not me) like it for dragging jigs and platics too
Copoly: Also versatile line, neutral buoyancy, mediocre sensitivity, inexpensive:
Topwater, cranking, spinnerbaits, chatterbaits, jerkbaits
When it comes to leaders, I don't use them on casting gear anymore. For me, they're just more trouble than they're worth the majority of the time. (On spinning reels I'll still use them though)