Basically you're going to want to go full crit/det for the best weapon, it will be very expensive since you need 11+ crit 4s and 8+ det 4s in the end. It's up to you if you want to add some accuracy, spell speed or piety to make it cheaper.

You will start out using grade 1 materia and after 8-11+ materia it will go up to grade 2.. then after 8-11+ grade 3.. then 8-11 grade 4 for a total of 75 materia infused.

There is no way to tell you exactly how many materia you will need since you can fail the infusions and may require more of a certain grade. If you fail an infusion you lose the materia but you do not lose the alexandrite.