The NPC will let you select an enchantable armor from the three main categories of Non-Slotted Armor, Slotted Armor and High Grade Armor. Each category has a different success rate. The success rate of the armor enchant and the rate of getting a +1, +2 or +3 stat are independent of each other. Chances of getting a simple success is much higher than getting a +3 stat. But keep in mind a success ensure you keep the armor even if you are not happy with the stat added you can use the armor for another try.
It is worth noting that chances of getting each of the 6 stats are the same, nothing in the NPC suggests that getting a +1 STR is any more difficult than getting a +1 LUK.