I was wondering if there was anyways, except by forbidding every low quality weapons, to make sure that each dwarf will always pick up the weapons of highest quality available.
In the newer versions (specifically 0.31.16 which I'm currently playing), you can specify an individual Dwarf's equipment by type, or even down to the specific item. From the (current at the time of writing) Dwarf Fortress wiki:
In the military screen, press n to open the uniforms tab. Each listing under the 'Uniforms' header is essentially a pre-designed set of equipment that you can quickly apply to any individual soldier or entire squad, much like a template. You can create new uniforms if you want and add or remove items from any uniform set by navigating this menu. Uniform templates are only created in this tab, not applied.
While still in the military screen, press e to open the equipment tab. The default sub-tab, 'View/Customize will be open. In this screen you can select individual dwarves and apply individual pieces of equipment to them, from Armor, Leggings, Helms, Gloves, Boots, SShields, and Weapons, as well as Material and Color depending on the piece of equipment highlighted. To select a specific piece of equipment (such as an artifact), select 'specific _____' under that equipment type (eg. 'specific armor' in the Armor field); for your convenience, highest-quality equipment is listed first.
Always? Not aside from forbidding all lower quality weapons. However what you can do is build a stockpile near the barracks limited to high quality weapons, and that will increase their likelihood of picking up the good gear. This is also true for armor. For further ensurance make your barracks and area around it lockable, get your dwarves in there, lock the doors, then reassign equipment.
NOTE This was true in 40d. The latest version may have added a simpler means of doing this, but I am unaware of it.