Cobalt for tool heads (fastest speed),
Manyullyn for weapon blades (highest base damage),
Manyullyn for tool rods (highest handle modifier),
Thaumium or Paper for anything else (extra mod slots, you can stack multiples with paper, only one thaumium part will count but it is good for extra tool HP along with the extra mod slots)
Many for tool rod is kind of a waste of resources. Slime rod has only slightly less handle modifier (second highest in the game), and that really only applies to durability which isn't nearly as relevant once you can put something like Mossy or Fluxed on your tool.
Cobalt is the fastest base material for tool heads. So if it is anything other than a sword, this is pretty much the go-to material.
Manyullyn is the best material for sword blades because it has the highest damage output of any material. Making a scythe blade out of Many also makes sense if you are using it as a weapon against the masses.
Thaumium and Paper both give an extra modifier, and Thaumium otherwise has the same properties as Iron. So using Thaumium as a plate won't cost you too much in statistics but will provide an extra modifier. It also makes an excellent rod since, as previously mentioned, durability is kind of not an issue after you are at this stage of the game. Paper is excellent at making bindings, guards, and other items that don't really affect the stats of a tool or weapon.