On all of my characters, I don't care what class, I take Engineering. Why? Because you can buy everything else.
If you're an Engineer and you need an enchant, you can buy it.
If you're an Engineer and you need a potion, you can buy it.
If you're an Engineer and you need a piece of armor, you can buy it.
If you're NOT an Engineer and you need a piece of Engineering, sure you can buy it, but it's not like you can do much with it. Most Engineering (Read: The most useful items) require the Engineering skill to use.
Except for a few exceptions here or there (BoP Blacksmithing, Leatherworking, and Tailoring items) you can buy just about anything you want. Besides, most of the BoP items you can craft are usurped by end game content eventually.
As for my other primary profession I usually do Mining. With a Hunter I might make an exception and go Skinning/Engineering. I do this because Hunters are typically not my first character I'll be making on a server, alowing me to already have some liquid, a regular income, and ore on another character. Also Hunters have the wonderful ability to Track Beasts which makes Skinning ever so fun and easy.
If you can make a profit elsewhere, Engineering is the greatest tradeskill, in my opinion.