Choosing the correct set of banjo strings for your instrument have a big effect on the tone and playability of your banjo. No specific set is the best. Every player has their own personal preference of what they like. The different string gauges, material used, the way the strings are manufactured, coatings, and the way they attach all effect the way they sound and play.
The first thing to look at is to make sure you have the correct set for the type of banjo you have and the tuning you are using. There are dedicated string sets for the specific type of banjo you are using (5 string, tenor, plectrum, 6 string, banjo uke, etc.). The different types of banjos can have different numbers of strings, tunings, scale lengths, and ways to attach to the tailpiece.
You do not need to change your strings to tune your banjo to most alternate tunings, but some tunings are different enough that a different set of strings should be used.
One example of a different tuning where you should use a different set of strings is open E tuning (E, B, E, G#, B) on a 5 string banjo. In this tuning you are tuning the banjo down so low that with a standard set of strings the string tension can become so loose that the tone and playability of your banjo suffers. We recommend using the Deering Julia Belle strings when playing in this tuning.
Another tuning where you should use a different set of strings is Irish tuning (G, D, A, E) on a tenor banjo If you are tuning your tenor banjo in Irish tuning , you should look for a set that is meant for that tuning as oppose to using a set that is meant for standard tenor tuning (C, G, D, A). This is because the string tension will be so much looser (similar to what happens when tuning a 5 string to open E) when tuned to the Irish tuning, so you will want a heavier gauge string to compensate.
Now that you have found packs of strings that are meant for your type of banjo, you might find different gauges available. When searching for 5 string banjo strings, you will generally see the following gauges:
You will probably also see some other specific sets that are generally custom gauges that artists use or are meant for a specific tuning.
Most banjos will come from the manufacturer with light gauge strings as they are easier to play. They also have a little bit more brightness to them. While heavier gauge strings will have a "fatter" tone - or little bit more tonal depth. They can be a bit warmer. They also allow the player to dig in with a harder picking attack, thus producing a bit more volume.
Before changing to a heavier gauge string, you should check the manufacturer's recommendations to make sure your banjo can handle the extra tension on the neck a heavier gauge string would bring. Deering recommends not to use string gauges heavier than their light gauge set on their Goodtime banjos.
Strings can be made of different materials such as nickel plated steel, stainless steel, nylon, phosphor bronze (used only as the winding on wound strings). 5 string banjos generally just have one wound string (the 4th string) as oppose to 6 string banjos usually have 3 wound strings. On banjos the winding is almost always roundwound. Guitars offer a number of different winding types.
For a musician who loves their banjo and loves practicing and playing, enjoys the nuances of technique and the magic of the emotional communication in playing...