Null weapons have 2 effects:

The first improves all weapons of their type by 1.3x atk and 1.45x HP
The second act like skills from normal weapons, but requires 6 weapons of that type in the grid (including themselves) to activate. The actual skill depends on the type of the weapon in question. The best ones are glaives (Assault++/Barrage++) typically used in water grids, spears (Assault++/Defender++) typically used in fire grids, and hammers (Assault++++). Bows are also decent (Assault++/Stinger++).

For the main three in particular, it's basically a no brainer if you can meet the requirements since they have good skills and will give you a ton more stats. The other weapons are more situational and depends on your grid/stats and what you want/need.