Here is a brief overview of some of your options: covered, standard, stability, and webbers.
Hide or calf skin covered stirrup leathers are my general recommendation for most situations. What I love about them is that they don’t stretch out overtime as they have a nylon interior and the leather is soft and won’t rub flaps that are also soft leather.
If your flaps are standard hide leather, then hide leather stirrup leathers work well and are less expensive. Know that standard leathers can stretch unevenly over time. Most often the left stirrup stretches out from mounting so make sure to check their length for symmetry regularly and switch the right and left each time you condition your saddle.
Stability stirrups come down to personal preference. Try some from a friend before you buy them as some folks really love the feel of the wider leather under their leg and some riders much prefer standard stirrups. If you like the feel, they can contribute to greater stability in the lower leg.
Webbers, sometimes called t-bar stirrups, have a t-bar buckle down towards the stirrup iron. This means there is no buckle or bulk under your upper thigh since a loop of leather goes over the stirrup bar. If you feel the buckle under your upper thigh or ride in a monoflap saddle, try a webber. Since the sizing is different, measure your regular leathers from the buckle to the hole you commonly use and then divide by two. Order a pair a few inches longer so you have room for adjustments.
What stirrup leathers do you like?