No matter what style or what genre of piano playing that you are in to, you need to be mindful of the fingering that you use. This doesn’t mean that there are a rigid set of rules that must be adhered to. Actually the only rule that I have ever heard is one that actually makes a lot of sense.
The rule in which I refer to is the rule that you don’t play a black note with your thumb. This is simply because our thumbs are shorter than the rest of our fingers and it is further to stretch for the thumb to reach a black note. This rule is broken on a semi regular basis because sometimes the piece or section of music just won’t work unless you use your thumb. The real rule should be: don’t use your thumb on a black note unless you have no other reasonable option.
This might sound obvious but I have seen a number of self taught piano players that don’t use all ten fingers. I know that it is easier said than done, as often people’s ring fingers and little fingers are weaker than their index and middle fingers, but it is really important that you learn to use all ten fingers. For most people, it will probably take a few months to develop the strength and independent function of any weak fingers. This will definitely enhance your piano playing ability in ways you can’t even imagine.
I have to add here that if you have a finger that is deformed or has arthritis to the point where it has become immobile, then obviously not using that finger is probably for the best. I have met a number of people over the years that had obtained an injury to their little finger years ago and now the joints don’t move at all. If I have just described one of your fingers, then I suggest you try and make the most of the other functioning nine. Having a finger that does not function normally is not a deal breaker. I once knew a violin teacher who had part of a missing finger on her left hand and she learned to hold down the violin strings with the stump of that finger. Basically, do what is reasonable for your circumstances.
The next comment that I would like to make is that if you see fingering on printed music, then usually that is the best way to go. People in the know spend time and effort working with the fingering indications so that it makes it the easiest and most effective way to play. Probably about one percent of the time, I will disagree with the fingering indicated and change it for a student, so it is more functional.
Whatever you do or not do, please consider your fingering that you are using for any piece of music that you play. You might find that your music sounds better by tweaking your fingering.