I think that Blacksmith Background should give to the PG at least 4 level-0 Formulas for blacksmithing items, because without the Formulas the Skill Feat is useless
"You can get access to the formulas for all common items in the Equipment chapter by purchasing a basic crafter’s book (see page 184)."
The cost: 5 sp for the book and 50 sp for the artisan's tools.
Thanks, I've missed the item
The Basic crafter’s book is only 1 sp.
Yes. the 10 sp (not 5) is for a blank formula book, which you will need for expert and higher level formulas.
Starting out as a trained smith, you need the crafting skill, trained in that skill, the basic crafter's book, and the standard artisan's tools. The cost of the latter two comes to 51 sp, about 1/3 of your starting money.
Blacksmith background gives you two ability boosts, one to strength or intelligence, and the other free. You also get Specialty Crafting (Blacksmithing) which is why you need to be trained in crafting, and you get a plus two circumstance bonus when using that skill to craft "durable metal goods, including metal armor".
You can increase your crafting skill to Expert at level 3, at which time you'll need a set of Expert artisan's tools, which will cost you 200 sp.
You probably also need a repair kit (30 sp) and eventually an expert repair kit (150 sp).