The Monster Hunter is intentionally split between martial skill and knowledge.

Strength

Strength supports heavy melee weapons, Athletics, and direct front-line builds.

It is especially natural for a Carver-style character.

Dexterity

Dexterity supports ranged and finesse weapons, initiative, Armor Class in lighter armor, and one of the class's saving throw proficiencies.

A ranged or mobile Hunter normally uses Dexterity as the main attack score.

Intelligence

Intelligence is the signature nonphysical ability.

It supports monster knowledge and powers important class mechanics.

Expert Strike lets Intelligence improve both attack and damage rolls with weapons and Unarmed Strikes.

Knowledgeable Defense can replace saves forced by studied creature types with Intelligence saving throws.

Several Guild mechanics, especially Occultist, make Intelligence even more important.

Constitution

Constitution adds durability on top of the d10 Hit Die.

The Monster Hunter is deliberately sent against high-threat creatures, so a good hit-point pool remains valuable even for ranged builds.

Wisdom

Wisdom supports Perception, Medicine, and Survival.

The Monster Grimoire can also interact with Wisdom checks related to studied creatures.

It is useful but normally sits behind the main attack score, Intelligence, and Constitution.

Practical priority

Typical Dexterity Monster Hunter:

Dexterity → Intelligence → Constitution → Wisdom → remaining abilities

Typical Strength Monster Hunter:

Strength → Intelligence → Constitution → Dexterity / Wisdom according to equipment and role

Guild choice can shift the exact order.