Mining and Skinning are what I took on my new Mage, actually. Gathering professions are usually a good bet for making money when you don't have a higher level toon to send money from. As a singular Alliance character on an all-Horde line-up means all I could send over were a couple Heirlooms.
If you -really- want to work on engineering, be aware that you'll be needing to buy supplemental materials on the AH that mining/smelting alone won't be able to cover. So, that's the part that makes it expensive. My recommendation would be to keep Mining and Skinning until you're in Northrend, because money drops from the sky like rain out there. Between quests, their un-needed rewards that you can sell for upwards of 15g a piece, and the bonuses from doing random dungeons, you won't really need the gathering professions to earn your keep. Heck, doing the Sons of Hodir faction quest-line can earn you almost 1k and it only takes about a day to get through (less if you already have Artisan flying.)
So if you really want to work on engineering, figure out specifically why (like, if there's particular pieces you want to have that you can't get better from drops, or bonuses just from leveling the skill up so high), and then wait till you're lvl 70+ to start working on them. That way, if you need to farm for stuff, you can do so quickly and easily with an epic land mount (not to mention, not being bugged by nearby mobs), and you can easily afford the supplemental mats.