Engineering is very non-class specific. The items you create are more oriented towards giving any class an edge in PvP (like bombs), useful trinkets (like the  Gnomish Poultryizer) and creating epic endgame bind on pickup head items. Engineers can also make guns and scopes to put on ranged weapons to improve their damage output. There aren't any endgame bind on pickup guns or scopes though, so this alone is not really a reason to pick engineering - it would be a lot cheaper to just buy those at the auction house.

Unfortunately, most of the items created by engineering need an engineer to use, so the market for your products is very limited - and the other potential users will most likely be able to create it themselves. The exceptions are guns, ammo, arrows and scopes which can be sold to other players. The only problem is the current price of low-level ores, making the guns much more expensive to make than what any buyer would pay (because green items drop and are sold for less).

One of the excellent benefits of being an engineer is that you will be able to learn to transport yourself to either Everlook & Area 52 or Gadgetzan & Toshley's Station - depending on whether you specialise in Goblin or Gnomish engineering.

Most of the items made with engineering require materials gathered with Mining. However, engineering uses a lot of varied materials, so expect to stock up on leather, gems and cloth as well.

I'd definitely recommend taking up Mining as your other trade, as most of the materials mentioned above are gathered with Mining - and the rest you need you can buy from selling some of the bars and gems you find whilst Mining.