Welcome to the Forum!!
I am "old-school" and use products that are time-tested and do the job correctly with no damage to the leather itself.
I use glycerine bar or saddle soap...none of the "new & improved" products marketed today.
I then only use Pure Neatsfoot oil when a deep conditioning is needed, very lightly applied to renew and condition the leather.
I have watched to many of the new improved, advertised & hyped cleaners leave the leather greasy or strip natural oils and can ruin the beauty, the patina of leather.
I have also seen to many of these products used to often, to much and rot the stitching right out of a saddle = expensive repair...
Always use sparingly any cleaning and conditioning products...I just prefer "old-style" needing some elbow-grease over the newer easy use stuff...
So, my way of cleaning...
Water, as hot as your hands can stand to be immersed in.
Sponge, tack sponge or a real sponge that cleans but not scratch when used.
Wet the sponge, apply soap and make a lather.
Apply that damp, only damp lathered sponge to the saddle and rub to clean.
Rinse, wipe clean with damp sponge...repeat till all soap is off.
Change the water as often as necessary to allow you to clean and rinse well...
Let the leather air dry...completely.
Only, only if the leather feels dry, looks dry do I oil my leather goods.
Very light coats applied using another clean sponge...let it absorb and disappear into the leather before ever applying another light coat of oil.
When all oil is absorbed, then I use a old piece of towel that I buff the leather to a beautiful shine...
Never soak your saddle either with cleaning product nor oil as it will rot your stitches.
I only ever clean my saddle in the shade an dlet it naturally air dry.
I do wipe down with a cloth my tack quickly after a use especially if the horse was sweating...it is far easier to wipe off damp sweat than scrub dried on yuck off.
I always dip and wipe my bit off of saliva or debris so it not dry and become a irritant to my horses tender mouth and lips.
Remember a little goes a long way...
I enjoy cleaning my tack watching a good TV show...gets done what need done and is actually relaxing to me to clean my stuff. **Never, never use oil or conditioning on suede or rough-out leather as it can ruin it.** A special metal bristled brush carefully applied will clean and raise the small nap of leather fibers of this special kind of leather..