The truth, there’s no cut-and-dry answer. You have to weigh sensitivity and speed of the fall you desire in choosing the line. This will be based on presentation and the species you are fishing. Use all three to your advantage for better days on the water!
A general rule is Monofilament is more manageable of the three varieties. Its larger diameter and major stretch works best for bass or panfish presentations like wacky worms, etc., because they will fall much slower.
A couple rules with fluorocarbon. First, you must wet the knot when tying or it will fail. Also, don’t use it for topwater lures or presentations, because it sinks. Fluorocarbon falls much faster than mono. Use fluorocarbon when casting crankbaits, casting wacky worms, Texas rigging, or jigging for walleyes or crappies. It is pretty versatile.You can use it for jigging and almost every application.
As for braids, avoid wherever you need some stretch. Use braids for longlining, and casting crankbaits (in tandem with a 5-foot mono or fluoro leader). Any situation where you are cutting through weeds is custom-made for braids.