For years I used the small tins of shoe polish.  Made a nice shine but did not do much for the barnyard  dirt, mud, water, and etc . 

What do you use as a boot or shoe protection or polish ?

I use Sno-Seal a bees wax concoction. Works very well for water proofing and keeping the leather soft.

Mink oil, but it seems to need replenishing quite often. I also have little to no experience with oiling or protecting my boots...trying to break old, bad habits.

I'm with Irondragon, Sno Seal.  But you do have to use heat to melt it and get it to soak in.  It will darken light, e.g. tan, leather.

Polish is for just what it says, making things shiney.  Not very good for water proofing or protecting the leather.  It is a surface product.  I say this as someone who has polished a LOT of combat boots and low quarters.

GNM

I use neatsfoot oil on my leather work boots, it’s not a waterproof, but it’s the best I found for the underground utility work I did for 37 years 

Yep, Neat’s Foot oil (was a brand name back in the day, the only one using beef shins and thus the only one that wine the US military contracts) which is the clear, thin fraction of tallow.
I also use olive oil, which is what the Smithsonian uses on its leather goods.  

I also use snow seal on leather and cotton fabrics (tarps and wet wether gear) that I want to make water resistant. 

oils get into the leather and lubricate the fibers, making them softer and resistant to drying out and cracking.
Glycerin is useful in restoring dryer out leather as it is hydroscopic. Not only will it attract moisture it will also fallow  moisture into the leather. 
land products like Snow Proof and boot way generally seal the surface shedding water.
as I had enough of polishing boots in the service myself, so I get oil finished boots and give them a fresh coat of oil fallowed buy a coat of snow proof (gets wet in Oklahoma, but back in AZ it was a good cleaning with saddle soap (glycerin) and oil. My old combat boot days started with a cleaning and light oiling with black polish and generally a soft brush shine. As I was not the best troop I wasn’t above just blackening them and carrying the uniform standing orders. My favorite was one NCO who said “you have a writhed problem Stevens!” To which I responded “I don’t have an attitude problem Sergeant , I have a bad attitude!” That ended about as one would expect, lol

Obscure etymological factoid:  A "neat" is an Old/Middle English word for a cow.  It has pretty much fallen out of use except for Neatsfoot Oil.  I have cooked a 17th century recipie for tongue which was titled in the original "A Neat's Tongue Stewed."  It was very good and a number of people told me that while they normally didn't like tongue that this was good and tasty.  You do skin the tongue which helps to change it into a piece of meat rather than a piece of a dead cow.

"By hammer and hand all arts do stand."

I always liked the crunch of the rind, mom cooked it for sandwich meat back when it was cheap. But lingua is bomb toco and burrito filling as well