To level smithing the quickest, you need to use the most the expensive parts to unlock recipes.
Here you can find the list of all parts with its values of the most expenisve type of weaponary in smithing: Two-handed weapons.
How to use the guide
The values represents the value of the swords crafted with that specific part.
Meaning, that in each craft, 3 of the following parts were used, with the 4th one being changed to one from one of the tables:
Ridged Short Kaskara Blade
Tapered Desert Guard
Tool Grip
Saber Pommel
Blade
Guard
Grip
Pommel
Why are numbers used instead of weapon part names?
Because I was too lazy to fetch them.