Here are a few general pieces of advice on economically improving blacksmithing skill.
As this is intended to save you money, buy only the materials you are sure you will need. If you run out, buy more. It is always more cost-effective to gather your own materials, rather than buying them. That is why mining is often recommended to blacksmiths, although you may instead have a mining alt. Also avoid having extras, but if you do, try to sell them back on the Auction House.
For leveling, select items that consist of fewer and less diverse materials. For example, plans that use one or two ingredients like [Copper Chain Pants]. This will economize materials.
If you have a choice of what to produce, try to make a diversity of items. This will increase the chances of selling the leveling trash at the Auction House and return some money.
Make items only when they are orange and yellow, especially if they require many materials.
Try not to make BoP items for skill-ups, including blacksmithing specialization items. They can be sold only to vendors. No reason to waste money.
Don't miss stones, keys and rods if they improve your skill. Stones are generally low cost to make while keys and rods can bring money.
Coarse Grinding Stones are not a guaranteed point after skill level 90, but you need a very large number of grinding stones for later items so you might as well make them now. Heavy Grinding Stone is not a guaranteed point skill after level 130, so leveling to 150 with them can be very expensive/wasteful.
Expert Blacksmithing
Expert Blacksmithing allows 225 maximum skill, requires level 20 and 125 skill.
With Steel Plate Helm requiring Citrine to make, it likely will need to be replaced with something else in order to keep the economical part of this guide valid.
Artisan Blacksmithing
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Reason: In patch 3.1.0, recipes for Thorium Armor and related items became available from trainers, no longer requiring a drop or AH-bought recipe. These are likely more cost-efficient than some of the Imperial Plate listed here.
Artisan Blacksmithing allows 300 maximum skill, requires level 35 and 200 skill. The Imperial Plate plans are obtained via quests from Derotain Mudsipper, by turning in Thorium Bars. A total of 30 bars are required for these plans. The 440 bar total includes this.
NOTE: It may be more efficient to craft Thorium items (starting with [Thorium Armor] at skill 250) which can be learned from a Blacksmithing Trainer. These are mostly more efficient than crafting Imperial Plate items so check Thorium items first.
If you cannot find [Plans: Mithril Spurs], the Thorium Bracers (or Belt) can be made from 260-265 instead. The total mats are 40 thorium bars, so it is also worthwhile to compare this cost to the cost for the Spurs plans plus the mithril.
Master Blacksmithing allows 375 maximum skill, requires level 50 and 300 skill.
A peculiarity of improving skill from 300 to 375 is that trainers do not teach all the required recipes for this range. You must buy from vendors or even farm some recipes to fill in this lack. Faction standing also becomes much more important.
The general course of action is to make normally trained Fel Iron items from 300 to 335 skill level. After that, you will need to buy adamantite items' recipes from your faction's and/or neutral vendors like Aaron Hollman. With these recipes, you may reach 350 skill. Then several bifurcation points come.
It should be noted that once you achieve level 68 and 350 skill in blacksmithing, you can immediately go to Northrend and train Grand Master Blacksmithing and begin to craft the low cobalt recipes, thereby removing the need to farm or purchase additional Outland materials or recipes. However, you may choose to instead continue with Outland trainers and recipes.
Blacksmiths who choose to skill up in Outland after 350 points have to make a few other decisions. Maybe the highest cost way to 375 points is to produce trained [Felsteel Whisper Knives], and switch to blacksmithing specialisation BoP items after 360.
An important decision of choosing to ally with either Aldor or Scryers specially imports for blacksmiths seeking to skill up in Outland. Both factions sell 4 reputation-dependent recipes (up to Exalted) for items that you can make for skill-ups until 375.
Also Plans: Felsteel Shield Spike requires skill level 360 and revered reputation with either Honor Hold or Thrallmar. Becoming green only at 380 this item looks like a cheap way to finish blacksmith`s training in Outland.
And of course getting some lucky drops like [Plans: Felsteel Gloves] or buying them from the Auction house would probably make some leveling easier.
NOTE: Currently, the table below involves reputation requirements. This is just one of many ways of progressing in blacksmithing.
Allocate 30 Adamantite Bars for reaching 350 skill level with [Lesser Ward of Shielding]. Considering that it turns green after 345 you have some chance to fail in midway. In this case, you may continue with Adamantite Plate Bracers.
Same story as with Lesser Ward of Shielding. Allocate materials for 30 Adamantite stones and use Adamantite Breastplate if you fail to achieve 360 skill level.
The key to leveling blacksmithing in Northrend is to farm the plans for the Reinforced Cobalt pieces. These use only 8 Cobalt Bars and 2 Crystallized Water for each item, require 375 blacksmithing to make, and stay orange to 395 for the shoulders, 405 for the helm, 410 for the legplates, and 415 for the chestpiece. Each Bind on Pickup pattern is dropped by a single specific mob.