I believe stats like STR/ATK/CRT should be native to gear and materia should add stuff like what Altanas posted.

Refresh +3
Regen +4
Damage taken -5%
Cure Potency +4%
Double attack+3%
Store TP+2%
Occasionally absorbs HP
Chance to Inflict Poison/Paralysis/Curse when attacked.

And weapon/shield exclusive stuff like:

Adds Ice Elemental damage to attacks.
Chance to reflect 3% of damage taken.
Convert 3% of Damage blocked to MP.
Increase piercing damage.