You are going to get many suggestions. Glycerine soap & Passier Lederbalsam are my tried and true favs. The trick to beautifully maintained tack has less to do with what products you use, and more about how often you actually use them. Never let the dirt get out of hand and condition as often as necessary. Oil sparingly.
Rule of thumb: clean/ wipe down frequently, condition regularly, and oil sparingly.
If something is really dry- I will clean it, oil it a few times lightly (never soak/dip!), and then I put a nice coat of Passier lederbalsam on top to help seal it in.
Avoid all-in-one cleaners like horsemen's one step at all costs, they frequently have ingredients in them that are not good for your leather long-term and I have found them to be sticky/ leave residue/ build up.
Scent a tack, castile soap, the Voltaire cleaner if my tack is a bit dry and Voltaire conditioner. The conditioner its much like other lederbalsams, but it doesn't leave the tack greasy or tacky and I like the smell.
If filthy dirty first use a mixture of warm water and a "glug" of ammonia. Use a brush like a nail brush to loosen the dirt and be sure you get the dirt off the tack by lifting it off with a damp cloth (or folks may frown on it but I have put tack in water to rinse the dirt off).
With standard dirty tack I use kirks castile soap with a brush.
After the tack is clean, I use Lederbalsam (just amazing stuff). I like to let the tack sit in the sun so it soaks in well.
After lederbalsam soaks in finish off with glycerin soap.
When I am being a good tack mother, I wipe my stuff down after every ride with a mixture of liquid castile soap (like Dr. Bronners mixed with 2 parts water). I use cut up t shirts as tack wipes and then wash and reuse.
But sometimes I fall of the wagon. Haven't had to do the ammonia treatment in a long time but it does work when you have or inherit dirty tack.
All my tack looks nice. But since I don't like to clean I normally ride in a biothane bridle- can throw it in the washing machine and it comes out looking like new! Only use my nice leather bridle for shows so it stays quite pristine!
I used Ledercombi to clean and Lederbalsam to condition, both by effax. I oil as needed or at least 2 times a year. Occasionally I use Leather CPR on my martingale and halter when I'm too lazy to do the whole process. I clean tack once a week, and wipe down with a barely damp cloth after each use.