What's the difference between mono, fluorocarbon and braid?

Can someone explain the difference between mono, fluorocarbon and braid lines and when I would use which? I just got into fishing this summer and it seems like there are so many options. Curious if I should change mine.

Basic line characteristics

Monofilament Line aka Mono:
 Affordability
 Availability
 Most widely used line
 Larger diameter
 More stretch
 High visibility
 Floats

Braided Line:
 Most strength
 Least stretch
 Smallest diameter
 Reduced visibility
 Floats

Fluorocarbon Line aka Fluoro
 High strength
 Low visibility
 Slightly more stretch than braid
 Considerably less stretch than mono
 Sinks

Other Things to Consider:
 Fish targeted
 Reel spool size
 Fishing Techniques
 Line color
 Knot tying
 Line cutting
 Abrasion resistance
 Leader or no leader
 Terminal tackle
 Casting ability