I'm "mom sitting" my mother this weekend; My brother is taking his wife to Bentonville to Crystal Bridges Art gallery where they are presenting Georgia O'Keefe paintings.... My sister in laws favorite artist! So I have the time to type on this subject, so please indulge me!
I got interested in hair jigs over 12 years ago or so and had a guy from Stockton, MO named Phil Schafer get me started with tying them. I always wanted to get the jigs to "match the hatch" and look as much like the prey as possible. This concept will get you more fish, to a point. The action is obviously another big factor because you need both pieces for the recipe. This is why I always try to get the proportion of the jig to be correct. Since jigs are basically tied in two pieces...the body and the tails , you need to make sure they are of realistic sizes. If you don't think this is important, then tell me why a Ned rig will out-produce a full Senko at certain times of the year? I tie two patterns for smallmouth, minnows and crayfish. The minnow jigs work well in moving water near a warm water influence of some kind. Since they don't have a weed guard, they have a high mortality rate. Just cast out and reel in slowly, be sure not to add any jerking/twitching motions (unless you're going for trout). The rabbit and fox add enough action just from the reeling in process. The smallmouth are usually totally infatuated with this jig and will either nail it at first sight (smallish fish), or swim up slowly behind it at a slightly faster speed and just open their mouth to overtake it (larger fish). This is why it's important to stay in close touch with the jig and not allow a loop of slack in your line.
Here is a picture of one of the minnow patterns I used to tie.
Right now I tie 5 to 1 more crawfish jigs than minnow jigs. I used to tie rabbit strip legs on the craw jigs but I don't do that anymore. Now I only tie about 1.5" of fox or raccoon hair and use my plastic craw for a trailer. Any small plastic trailer will work. Note: You need to really watch though to make sure they allow soft plastics in the area you're fishing. I usually don't use palmered crosscut rabbit anymore because once you wrap the strip on, you have no room left to run your soft plastic trailer up onto the keeper on the hook. You can do what Al does and "nose hook" the trailer in this case. I always use a weed guard on the craw lures. If you fish these jigs often enough with good quality equipment you will develop a feel where something seems a little out of the ordinary. This could be a fish! Like MOsmallies said, setting the hook is for free! so true...
The other day I noticed I had a .5" diameter piece of leaf that had been impaled by my hair jig hook and it felt like I was reeling in a small stick! I personally wouldn't use anything below 6 lb test for winter fishing, actually I normally use 8 lb, but thru fancy marketing strategies some line manufacturers might have a 6 lb test that is the same line diameter as the 8 lb of another manufacturer. I always go by the diameter of the line and don't pay as much attention to the pound test. A smaller diameter will be less abrasion resistant than a larger one. Always check your line for nicks, which I'm guilty of not doing myself. Concerning fluorocarbon, the fluorocarbon's surface finish is not as smooth as nylons, so moistening the knot before you cinch is super critical, more so than with nylon. The friction created during the cinching process will produce heat which will weaken the knot.
I prefer baitcasting equipment when throwing jig of any kind, even for jigs down to 1/8 oz. With a rod limber enough to load when casting a jig, its hard sometimes to pull a jig free from a rock, so a slightly stiffer rod will help but makes the casting of a lighter jig more difficult. It's a catch 22.