For an organist, this question is quite important. Correct organ shoes can help you to develop a better pedal technique. In some cases, the shoes can even determine whether or not some particular pedal line can be played or not.
The correct organ shoes should have a fairly narrow tip, so that you could play just one pedal key at a time. A very flat tip would give you some trouble in hitting the right notes.
The soles and the heels should be made from leather so that you could slide from key to key, if necessary. The heels should be about 1 1/4 inch (or about 3 cm) high for the optimum toe/heel technique.
Women's shoes are best with stretch band with buckle. It is not uncommon for women organists to use higher than 1 1/4 inch heels for organ playing. There are numerous stories about famous French women organists who can play virtuoso pedal lines with high and narrow heels. How can they manage that I have trouble imagining.
Whether you order professionally made organ shoes, or just find the similar ones in your closet, DO NOT play with shoes you walk on the street, running shoes, tennis shoes etc.
I've seen some people just use their street shoes for organ playing, but I don't recommend that for these reasons:
First, it is very important that the dirt from the street would not stick to the pedals. It can even make some damage to the construction and mechanics of the pedal board.
Second, if you use just regular street shoes, the heel might not be with the right height which in turn might make your pedal technique develop incorrectly.
By the way, I know some organists who play the organ without shoes at all... It might seem strange, but they use thicker socks so that their feet will not get cold, especially in the winter. They claim that direct contact with the pedals is the best.
But of course they can't take advantage of the heels which make playing toe/heel technique quite difficult. At any rate, it is better just to take your street shoes off and play without them until you find the right ones you will use specifically for organ playing.
Often organists use dancers shoes for organ playing which usually works well for pedal playing. So, where you can find the right organ shoes? If you want to get suitable organ shoes you can take a look at these shoes for women and men.
By the way, do you want to learn to play the King of Instruments - the pipe organ? If so, download my FREE video guide: "How to Master Any Organ Composition" in which I will show you my EXACT steps, techniques, and methods that I use to practice, learn and master any piece of organ music.