So. You have 2 different ways to craft stuff, and mostly you have to combine these two ways to get something useful.
The second tab is "Production". You should start here, and specifically with Refinement.
My list are way longer than yours because after a bunch of crafing levels new stuff will appear. First as red that you can't use yet, then they become more yellow, green and pale and that shows how much exp you get for crafting them (lowert the more pale they get, ending with grey and zero exp).
You should at least have Green Wood Planks, Dowels, Leather and Bronze in your list.
Make this stuff! Only reason not to make as much as you can is space and if you wanna craft on other characters. I usually at least make a bunch of each until they are all grey.
Then you need to make the parts! To make a pistol you have to craft both the barrel and the frame. They should both be in this list.
I wish that was the end of it, but sadly you have to make it have some kind of power!
So we have to go to Inscriptions!
All weapons need an inscription. The materials here depends on what stats you want the weapon to have. You have to craft the same tier of inscription as the weapon. For example Green Wood and Bronze go together, you can't craft the Bronze and Green Wood weapon parts and then add an inscription made from Soft Wood.
When you have these three parts you need to go to the Discovery tab instead.
Here your parts will show up and you have to combine them! This is only done the first time, after that the character knows how to make the item and it will be in the list under "pistol" (or whatever weapon you made). Only the chosen stat version will show up tho (like Mighty Pistol), the others have to be discovered separately.
The other stuff in this list makes things like sigils and you have to "discover" them to learn them too.
Here is an example of a random discovery.
Red icons means I don't have enough levels in this prof to use them (if I hover over them they say "Huntsman (400)" and I'm only 387 so that's a no go). If you can't match anything then you don't have the materials necessary (often it's those slivers and orbs and stuff that are pretty rare drops).
There is always a level to the discoveries, and the closer to your level, the more exp you get. Crafting already known recipes gives exp (as long as they are colored) but it's way less than discovering stuff. So for leveling you basically craft a bunch of pistol parts and then all the different inscriptions to discover all the different stat versions of pistols.