Here's the path I took to 405 Engineer.

**IMPORTANT NOTE**
---Several of the crafts below will be at Normal (Yellow) Exp rate, so take EXTRA materials just in case. I was very lucky with my leveling but on several other characters, it was super frustrating.
---Buy your materials from Auction House first then head to Dalaran, the trainer has all schematics, and you have Anvil right next to you.
---Get White Smoke flare from a vendor (https://wotlk.evowow.com/?item=23811#sold-by-npc). I suggest you go through Shattrath and then to either Exodar or Silvermoon (You can find the schematic and buy your mats from AH)
---Unless you don't mind spending extra gold, you could farm the materials on your own (It took me a few hours)
---Again, Total materials below are NOT ACCURATE; it depends entirely on your luck. I suggest you buy an extra stack, you can save the leftover materials or resell on Auction House. (Trips to and back from the Auction House are annoying.)
---My total receipt was around 1800 Gold, but I got some leftover materials that I can use on other character. Several materials have become very expensive (As of Jan 3rd - 6 AM Server Time)

1-43 Rough Powder
43-52 Copper Bolt
52-55 Arclight Spanner
55-64 Rough Copper Bomb
64-75 Copper Tube
75-97 Coarse Powder
97-100 Copper Mod
100-103 Target Dummy
103-106 Practice Lock
106-127 Bronze Tube
127-145 Heavy Powder
145-172 Whirring Gizmo/Bronze Framework
166-181 Explosive Sheep
181-187 Solid Blasting Powder
187-190 Micro Adjuster
190-199 Iron Grenade
199-202 Mithril Tube
202-217 Unstable Trigger
217-232 Mithril Shot
232-244 Mithril Casing
244-250 Hi-Bomb
250-262 Dense Powder
262-285 Thorium Widget
285-301 Thorium Shot
301-316 Fel Iron Bolts / Elemental Powder / Fel Casing (Feel free to skill up with Fel Iron Shots)
316-328 Fel Iron Bomb
328-337 Adamantite Grenade
337-355 White Flare
355-370 Cob Bar
370-376 Volatile Trigger
376-382 Cobalt Frag
382-391 Explosive Sheep
391-400 Froststeel Tube
400-406 Diamond Refracted Scope

Azeroth

9x Handful of Copper Bolt (1x Cbar)
1x Arclight Spanner (6x Cbar)
5x Rough Copper Bomb (1x Cbar/1xCBolt/1xLinen/2xBlastingPowder)
3x Copper Tube (2x Cbar/1xWeakflux)
11x Coarse Powder (11x Coarse Stone)
1x Copper Modulator (2x CBolts/1xCbar/2xLinen)
1x Target Dummy (2x CBolts / 1x CMod / 1xWool / 1x BronzeBar)
1x Practice Lock (2x CBolts / 1x Bronze Bar/1x Weakflux)
10x Bronze Tube (2xBzBar/1xWeakflux)
22x Heavy Powder (1x Heavy Stone)
5x Whirring Gizmo (2x BzBar/1x Wool)
5x Bronze Framework (2x BzBar/1x Medium Leather /1x Wool)
5x Explosive Sheep (1x BzFrame/1xWhirGiz/2xWool/2xHeavyPowder)
7x Solid Powder (2x Solid Stone)
1x Micro Adjuster (4x SteelBar)
7x Iron Grenade (1x IronBar/1xSilkCloth/1xHeavyPowder)

2x Mithril Tube (3x Mithril)
6x Mithril Shot (1x Mithril Bar/1x Solid Powder)
6x Unstable Trigger (1x Mithril/1xMageweave/1xSolidPowder)
6x Mithril Casing (3x MithrilBar)
3x Hi Bomb (2xMithrilCasing/1xUnstableTrigger/2xSolidPowder)
20x Dense Powder (2x Dense Stone)
9x Thorium Widget (3x Thorium Bar/1x Runecloth)
5x Thorium Shot (2x Thorium Bar/1x Dense Powder)

Outland

8x Fel Bolts (1x Fel Bar)
11x Elemental Powder (1x Fire Mote / 2x Earth Mote)
4x Fel Casing (3x Fel Bar)
4x Fel Bomb (1x Fel Casing / 2x Fel Bolt / 1x Elemental Powder)
3x Adamantite Grenade (4x Adamantite Bar / 2x Fel Bolt / 1x Elemental Powder)
18x White Flare (1x Elemental Powder / 1x Netherweave cloth)

Northrend

6x Cobalt Bolts (2x Cob Bar)
4x Volatile Trigger (1x Crystallized Water / 3x Cob Bar)
3x Cobalt Frag (2x Cobalt Bolts / 1x Volatile Trigger)
3x Explosive Decoy (1x Frostweave / 2x Volatile Trigger)
3x Froststeel Tube (8x Cob Bar / 1x Crystallized Water)
1x Hyperspeed Accelerators (6x SaroniteBar/4x Crystallized Air)
1x Diamond Refractor (2x Cobalt Bolts / 1x Froststeel Tube)

Total Materials: (Suggested-Min"Lucky")
18-6 Saronite Bar
90-67 Cobalt Bar
2-1 Eternal Water
2-1 Eternal Earth (Optional if you make Capacitors)
12-4 Crystallized Air
40-30 Fel Iron Bar
16-12 Adamantite Bar
30-11 Mote of Earth / 60-22 Mote of Earth (If you have smelting, you can save a bit of gold with 2x Primal Earth/1x Primal Fire)
50-37 Thorium Bar
50-36 Mithril Bar
10-7 Iron Bar
8-4 Steel Bar
60-42 Bronze Bars
50-29 Copper Bar
14-7 Linen Cloth
30-21 Wool CLoth
10-7 Silk Cloth
15-9 Runecloth
30-18 Netherweave Cloth
10-5 Medium Leather
30-20 Rough Stone
20-11 Coarse Stone
40-22 Heavy Stone
50-36 Solid Stone
50-40 Dense Stone
20-15x Weak Flux

-Blacksmith Hammer

Will test again using this list and will update.