Best type of keel
In terms of sailing ability nothing that we know of sails better than a properly designed Fin keel. They have less drag and they typically make less leeway and go faster. You can get the ballast down lower so in theory they are more stable for their weight. They are more maneuverable. They take better advantage of the high efficiency of modern sail plans and materials.
They have some disadvantages as well, many of these have been offset or worked around by modern technology but at some level they are still accurate critiques. They have less directional stability than long keel boats so the tend to wander more under sail. Since directional stability is also a product of the dynamic balance between the sail plan and underbody, in practice they may actually hold a course as well as a full keel. In general though you can expect to make more course adjustments with a fin keel. It is sometimes argued that it takes less energy to make these corrections so a fin keel may also require less energy to maintain course. This I think is a product of the individual boat and could lead to a debate harder to prove than the number of angels that can dance on the head of a pin.
Fin keels are harder to engineer to withstand a hard grounding and when aground they are more likely to flop over on their bow or stern. (Although in 37 years of sailing, I have never heard of anyone actually experiencing this.) Fins typically have deeper draft. They are easier to pivot around and get off on a simple grounding.
A shoal keel is just a keel that is not as deep as a deep keel. Today the term seems to be applied mostly to shallow fin keels. Shallow full keels seem to be referred to as shoal draft boats. (You guys notice that as well) A shallow fin is a tough animal to classify. I really think it has few of the advantages of either a deep fin or a full keel and has many of the worst traits of both full and fin. This can be partially offset by combining a shallow fin with a centerboard, which is a neat set up for shoal draft cruising. In fact if I was cruising in your area keel-centerboarder might be my first choice.
A lot can be done to improve a shallow fin. One way is to add a bulb. A bulb is a cast metal ballast attachment added to the bottom of the keel. They concentrate the ballast lower providing greater stability and sail carrying ability than a simple shallow keel. Traditionally bulbs were torpedo or teardrop shaped. They have been re-contoured to provide some hydrodynamic properties. These are also referred to as Sheel Keels(named for the man that invented and patented one version of this idea).
Since shallow keels need to be longer horizontally than a deeper fin in order to get enough area to prevent leeway. This means that it would generate more tip vortex and more drag than a deeper keel. The bulb creates a surface to turn the water aft and prevent it from slipping over the tip of the keel thereby reducing tip vortex. This does not come free since a bulb increases frontal area and surface area and there still has more drag than a normal depth fin.
Wing keels are a specialized type of bulb keel. Instead of a torpedo shaped bulb there are small lead wings more or less perpendicular to the keel. These concentrate weight lower like a bulb and properly designed they also are very efficient in reducing tip vortex. There has been some discussion that wings increase the effective span of the keel when heeled over but this does not seem to be born out in tank testing of the short wings currently being used in production sail boats. Not all wings are created equal. They potentially offer a lot of advantages, but they are heavily dependent on the quality of the design and I really think that many wing designs are not really working to their potential.
Wing keels have all of the negatives of a a fin keel in terms of difficulty of attachment and risk in a gounding. They dramatically loose lift in a chop. When you run aground (especially if heeled over) they are much harder to free. They are being way over sold in terms of performance. Depending on the model they typically have PHRF ratings 15 to 30 seconds a mile slower than the regular keel. That is significant.