TiCo2 did a decent job of making most tool materials useful and viable, when compared to TiCo. Rather than having tiered materials, the materials now have unique modifiers, which can greatly alter how a tool works for any given job.
I enjoy using Copper bindings on my pickaxes due to the extra XP given. I usually pair it with Mending Moss to greatly increase the lifespan of the tool. Using an Iron head gives the tool a small magnet effect, which is nice early game. Using an Obsidian Sharpening Kit will increase the mining level to max. As Cobalt becomes available, I sometimes swap to that for a head, since I usually have access to a magnet from some other mod by then which makes the Iron head obsolete.
Lumber Axe is made from Iron (magnetic), Copper (well established), Treated Wood (forgot the trait, but slow self repair), and Obsidian. Add some Mending Moss and Redstone and you're off to deforestation in no time. Depending on how my world is set up, AutoSmelt can be fun, as it now turns a forest into stacks of charcoal - I'm not sure if Luck plays with the output on that, but it's worth a shot if you're bored.