When you create your character, you should choose what types of weapons they can equip.  I would recommend that you keep it to one or two types.  Many of the Skills you can learn can be used to make and/or personalize and improve upon your weapons.  Generally, archaic weapons will become stronger through heraldic enchantment, while advanced weapons get technological upgrades...but sometimes you can do both!

Below are all the major types of weapons from the PSX game plus as many appropriate armaments I could think of, with their strengths measured relatively in a way that will aply throughout the game.  The maximum strength a weapon can have in any area is 6, and the minimum is 1.  Their overall strength will always add up to 9.  This is only for reference; I will create the specific weapons the characters come across by referring to these numbers or the numbers you work out when you create your own weapon.

Attack Strength refers to the weapon's ATP and general damage capability.  Attack Speed refers to the Dexterity bonuses it gives your character, if any, which will likely increase the number of hits it is capable of.  Magic refers to how likely the weapon is to give you a magical enhancement.  It will usually be an enhancement of your MAG stat, but weapons that are more magical in nature are also more likely to give other bonuses, such as halving MP.

If you would like to create your own weapon type, remember that mechanical weapons always have a magic value of 1. Also, making your weapon long-range will cost 1 point, and lastly, none of the three weapon attributes may be below 1 or above 6.