The challenge, of course, is getting to 375 engineering without going completely broke in the process. Usually Lootables is a nice place to start when leveling your profession, but their engineering guide misses a few money-saving opportunities, and they assume that you're just grinding for grinding's sake. If you have a specific goal in mind, you can get skillups for crafting the materials that you'll need later on.
I'm going to focus on 350 and up (since that's what I've done recently and remember well), but for the sake of completeness, I'll start at 300:
- 300-325: Elemental Blasting Powder, Fel Iron Casings, Fel Iron Bolts, and Fel Iron Shells. On my server, Fel Iron Casings are marginally profitable, though they don't move very fast at the auction house. The other items are not necessarily profitable, but you'll need at least 20 Blasting Powder for Smoke Flares (below), and you'll need at least 9 Casings and 12 Bolts for Adamantite Rifles (also below). The Shells will get you to 325 if nothing else will.
- 325-335: Adamantite Frames. These babies are profitable, and you'll need a bunch for Adamantite Rifles later on. Load up!
- 335-350: Smoke Flares. Recipes for these flares come in various colors. There's a green one available from the Cenarion dudes, and a plain one available in Area 52. They cost virtually nothing to make and will easily get you to 350. If you're patient, I hear they'll carry you to 355.
- 350-365: Felsteel Stabilizers, Khorium Power Cores, Hardened Adamantite Tubes. You'll need 8 each of the Stabilizers and the Power Cores for your flying machine, and you'll need 5 Tubes for Khorium Scopes later on. If you plan to make your epic goggles as well (and have the requisite Primal Nether), you'll want to make an extra 4 Stabilizers, 2 Tubes, and 1 Power Core, plus the goggles themselves. If you get above 365 while doing all of this, more power to ya.
- 365-370: Adamantite Rifles. This recipe is available from the engineering vendor in Shattrath, and it'll carry you up to 370. On my server, they cost 40g to produce and sell for 10g, so the loss per Rifle is 30g. (You did save those Bolts and Casings from earlier, didn't you?) I got a skillup from every one until they turned green at 370, and my sole attempt at 370 failed to yield a skillup.
- 370-375: Khorium Scopes. Five of these should hopefully get you the rest of the way. Make sure to use those Hardened Adamantite Tubes you crafted earlier. You'll invest about 150g worth of mats, and you can sell them for about 100g, so that's a 50g loss per Scope. That's more than you lost with the Rifles, but at this point, you'll probably need to make at least two Rifles per skillup, so the Scopes are the cheapest way to go. Here's the catch: The recipe is a BoP drop from Sunfury Bowmen near Manaforge Duro in the Netherstorm, so you'll have to grind them for an hour or so in order to get it.