Line weight is the most straightforward. Pick the lightest line weight possible for the environment and fish species in order to maximize casting distance and sensitivity. When I fish the spillway for Flathead Catfish I know that I am going to potentially catch a fish 60+ lbs and will also be fighting a very rocky bottom so I choose 80-100 lb line. If I am throwing beetlespinners to suspended Crappie I prefer 4-6 lb test. 

Line color is also simple. In murky water I prefer greens, in clear water I prefer clear line. Match the line color to the water color in order to minimize line visibility. 

Now to what confuses many anglers: line type. A few years ago almost all anglers used monofilament and it still remains the most popular choice today, however, in several circumstances and presentations there are better options. 

Monofilament

Monofilament was invented by the Dupont Chemical Company in 1939. It is quite simply a single strand of plastic of a certain diameter which gives it a tested breaking strength. Monofilament is cheap, has the slowest sink rate of the three line types, has the most stretch, excellent knot strength, is very manageable on all reel types, and is available in a multitude of colors and test weights. The primary disadvantage of mono is that it is highly subject to line twist and over time it becomes weakened by UV light and water absorption. Given these disadvantages most anglers change their monofilament lines at least once if not more often per fishing season. 

I prefer to use monofilament on most of my spinning reels given its low memory which makes it more manageble. Further given the slow sink rate, since it absorbs water, mono is an excellent choice for finesse fishing technique like wacky rigs, allowing the bait to suspend longer and drop slower when presented to the fish. 

Fluorocarbon 

Fluorocarbon or Polyvinylidene Fluoride, was first popularized as a leader material for saltwater applications in the 1970's and as the chemistry has advanced allowing for softer and cheaper production, fluorocarbon may now be used as a main line for a variety of fishing styles, not just as a leader or tippet. While it may look and somewhat feel like monofilament, fluorocarbon is a very different breed of line. The defining characteristics are its high abrasion resistance, fast sink rate, and low optical density. This last quality is what has attracted many anglers to it. Water has a light refraction index of 1.333, fluorocarbon refracts light at 1.41 whereas monofilament refracts light at 1.52. This means that fluorocarbon is much less visible under water, though not invisible as some manufactures claim, allowing  the angler to present the bait much more naturally. The density of fluorocarbon are also what give it its qualities of a fast sink rate and abrasion resistance. Unlike braid and mono, it does not absorb water and as such has the fastest sink rate of the three. This makes it very useful for deep water applications. Further this density allows the line to resist nicks from obstructions and the teeth of fish, in fact this property is what first popularized fluorocarbon as a leader material for toothy fish such as Barracuda and Muskie. 

There are certain disadvantages to fluorocarbon as well. First is the cost, a typical spool of line will cost anywhere from $14-30 dependent on the line quality and brand. Secondly is knot strength. The density of the line makes it susceptible to cracking when tying a knot. This can create a weak spot allowing the line to break upon hooking a fish. To avoid this, manufactures recommend lubricating the line first with water and using a palomar knot when tying on a lure. Finally, fluorocarbon is much stiffer than either mono or braid. This often makes it difficult to use on spinning reels, I will admit I have tried two different brands on spinning tackle both of which ended in frustration. 

I currently use fluorocarbon fully on only one rod. A pole which I have set up specifically for deep diving crankbaits. The reel is a baitcaster and I have had no problems with line management unlike on my spinning reels. The sink rate and abrasion resistance of the line allow me to achieve deeper depths and resist nicks from rocks or timber I may be bumping into. I also use it as my tippet on my #4 weight fly rod during trout season due to it low visability and plan on using it this year in the form of a leader during the walleye spawn again for visibility reasons. 

Braid

Braid is the oldest of the line types but is only recently making a comeback with modern anglers as increased material strength has allowed it to become much stronger as well as thinner. Braided line is made from man-made fibers such as Dacron, Spectra, and Micro-Dyneema which are woven together to make one line. Braided line has no memory, handles line twist very well, is very thin, has no strectch, and incredibly abrasion resistant. Braided line will work on both spinning and baitcasting reels, though its limpness will sometimes cause severe birds nests in both reel types. The two primary advantages are its abrasion resistance and thin diameter. The thin diameter allows for exceptional casting distance. For example Power Pro brand braid in 20 lb test is only .009" compared to 20 lb monofilament at .016". This allows not only for greater casting distance but also the ability to use heavy line on spools which would otherwise be to small to accommodate heavy test mono or fluorocarbon. The abrasion resistance and strength of braid is phenomenal. It is very difficult to cut without scissors or a knife, no using the pliers here. This translates into a line which is great when fishing heavy cover such as spillways or heavy timber. The final reason to consider line is the lack of stretch. If lures will be far away from the angler this will result in more solid hooksets. 

Braid also has many disadvantages. First is it is the most visible line type. Clear water applications or use with line shy species is very limited. Secondly, the small diameter causes a lure to fall through the water faster than it would on a similar test weight mono. While this may be desirable for some applications in others such as finesse fishing, it will prove a cumbersome inconvenience. Finally, as alluded to previously, the limpness of the line can cause bad birds nests, or knots in your line. A higher quality reel can prevent a lot of this but they are unavoidable from time to time. 

I primarily use braid when fishing for large, aggressive fish species: flathead catfish, muskie, and northern pike. These are active, aggressive feeders who quite honestly are not timid when it comes to line recognition. The small diameter allows me to cast further and the abrasion resistance gives me more confidence to cast into areas where I would otherwise lose my tackle. In murky water I also use braid to fish heavy timber for bass, when pitching jigs or spinnerbaits. The murky water I believe makes up for the line visibility. 

In summary, there are no absolute right line choices for all conditions and all anglers opinions will differ slightly. I hope I have at least illuminated the subject and also shown you why I have made my choices. Experiment will all three and learn the characteristics for each and I promise you will become a better angler.