Where do you start with jig fishing? First off you start by matching the depth you want to fish to the head size. Fall rate is everything in a jig, as well as head shape. In a situation that you're dragging a jig you want a head that is knocking on anything it contacts, you want it also, to have a line tie that is not going to get hung on every little rock it contacts. An Arkie head is an excellent option for a casting jig. It's a versatile head style that casts easily and has pretty reliable bottom contact. (Which, on that note, is something to consider. In so many situations, I tend to throw conventional wisdom out the window. I fish heavier than normal jigs to feel bottom content, me create more disturbance. I fish more 3/4 and 1 ounce jigs in shallow water than lighter weights. I also feel that it creates more instinctive type bites on the fall.)
One of the next factors to consider, as has been mentioned is color. While, again, I tend not to subscribe to traditional theory of color, I do have some standard colors I fish. Generally Green Pumpkin with orange is my first clear water color. I use Okeechobee in a wide variety of clear and mixed water situations, and dirty water I lean more toward black blue and black purple chartreuse. Where I will adjust colors is my trailer choice. I typically am going to match my trailer color to my skirt, except when I don't. I will use an offset color like a Falcon Craw on a black blue jig in dirty water where there are rusties. I will use a blue bug trailer on a Peas And carrots skirt in cold clear water. Things like that you get a feel for after seeing craws in new waters you fish.
The next determination to make is profile. Profile is somewhat determined by the head style and size, but more importantly it is determined by the skirt shape and trailer choice. Skirts on a jig can be a full, flowing 60 strands, or they can be cut back to flare and strands pulled out to make it thinner. I usually start with a jig skirt that is slightly longer than the shank of my hook, and usually it is full. A large profile, if you will. When I modify a jig skirt, the first thing I do is trim the length. If I want the jig to be just a more compact profile, what I do is trim a few strands from the forward portion of the skirt, the part pointing towards the head that folds back. Trim a few of those out, and then loosely hold all of the strands between my index and middle finger, along with the hook, and trim them dead even with the bottom of the bend. If I want even less profile, I will trim or pull a few of the underlying strands out of the skirt. The second aspect of profile is somewhat preference, and somewhat based on experience. Choosing a trailer for a jig needn't be more complicated than, initially, choosing whether you want a large or small profile. For a standard trailer, I use a rage craw. Almost exclusively that is my first choice. I will bite off a notch of the tail section, and start there. If I want thicker, heavier profile, I use a rage bug. If I want a slimmer profile I lean towards a DB rage Craw, or a menace. In the case of a swim jig, my choice of trailer is a swing impact or similar, or a menace.
So, that's a starter. Jig head styles are somewhat subjective. There are no hard and fast rules that state what must and must not be fished in a given application. What you will find over time is that you're going to prefer one over another based on performance in a given situation. I have Arky, Alien, Punch, Football, Flip, Cobra, swim, grass, flip swim, and finesse styles. They're all good for different things. They're all pretty specific in how I use them. The most versatile is the Arky. I'm not really partial to one brand or another, some are better for specific situations, some have better hooks. Siebert builds a good jig. Strike King builds a good jig, as does Dirty Jigs, and several others.
One last note; someone mentioned a finesse jig being a good starter. I disagree with that assertion. They are rather easily hung, and generally don't have a very good feel as a starter. Less surface area of the jig in contact with the bottom is the primary reason for that. The second reason I don't like to start someone on a finesse jig is they have a very different fall rate. They're more difficult to effectively modify that rate, and equally difficult to get a large profile. They have their applications, but not as a starter.