How can I improve the Barrel material of this character?

Thorn is very right. Play with them.

I have already tried to explain the way I understand learning shader nodes here. There are other awesome answers in the thread as well.

You can definitely find loads and loads of video tutorials on creating procedural wood in Blender. I don’t think you need to create real complex procedural wood for this, but you can find some great tutorials for it and some of the wood techniques are really great for learning procedural texturing in general, especially the ones that show the technique with simulating tree rings, like this one for example(but I haven’t watched it just skipped through to see the volume with the rings, so no idea how good it actually is, but I suspect it’s going to be good). So I don’t think you need to use that technique here for what we see in the reference(actually I am not sure what we see there I would look for better reference as well if possible) and simpler techniques will work, but I think it’s worth watching. And it’s also quite interesting. I mean simulating tree growth rings with math? That’s awesome if you think about it, isn’t it?..