Exactly how does Adventurer Conqueror King differ from B/X D&D, Labyrinth Lord, and Pathfinder? If I wanted to begin playing with a system-light D&D, preferred ascending AC, and wanted something "out of the box" without a lot of rules-fixing, what would you recommend and why?
It's design is basically an expansion of B/X D&D.
It still has race as class but expands the number of racial classes into a section labeled Demi-Human Classes for example there is a Dwarven Vaultguard and a Dwarven CraftPriest.
It adds proficiencies which are skill and abilities mostly non-combat oriented. They represent something that the character is better at than a non-proficient person.
The heart of ACKS is the campaign section where the author add several subsystems that allow the character to impact the setting beyond the usual adventuring locales. These include
The treasure type system has been tweaked to work with the various assumptions on wealth and income outlined in the above subsystems.
ACKS is closely derived from B/X by way of Labyrinth Lord. Ascending AC is one of its differences as explained here. The esteemed Mr. Conley does a good job of describing the other things ACKS is designed to do "out of the box", although I think the rules for running a thieves' guild and sending out your underlings to do hijinks are also worthy of mention.
You could separate race from class in Adventurer Conqueror King most easily by allowing any race to become any class. You might then want to define racial bonuses separately - right now they're baked into ACKS' non-human racial classes. (You could also leave racial effects as part of the setting instead of the rules; as it stands, humans don't get bonuses but are much more likely to enjoy positions of power in society.)
It'd be straightforward to adapt racial bonuses from any other D&D-lineage system. If you wanted to get more into it, the ACKS Player's Companion has a class design system that lets you create custom classes balanced for factors like racial bonuses, with a couple of examples of new race/class combos. The assumption is still race-as-class, but you could just as well use the system to design class features and racial bonuses separate of one another.