Well, if you're a student, then whatever is available at your computer labs should probably be what you learn.
The industry standard for mechanical engineering is Pro-Engineer. In my opinion, it isn't very user friendly, and is a bit of a pain to learn, although their latest edition: "Wildfire" is getting better.
Pro-E has the ability to do finite element modeling through Pro-Mechanica which is an add-on.
Solid Works and Solid Edge are two middle-of-the-road packages. I haven't used them personally, but from the demos I've seen they seem to be much easier to learn, but may not be as powerful as Pro-E.
Catia is another high-end package used almost exclusively in Aerospace and Automobile applications. I think Boeing and GM use this software. It looks incredibly powerful, but the ticket price is enough to make any small company blush, let alone a student.
I'm not sure what they use in typical structural engineering firms.
If you have to buy something yourself, and a student version of a real solid modeling package isn't available to you, you could always give AutoCAD a run around the block. It's got solids capabilities which would let you learn how to build objects in 3D. The real drawback is that plain-old autoCAD isn't parametric, meaning once the object is designed, you can't go back to modify any values. On the other hand, AutoCAD is the industry standard for 2D drawings, and definitely is much better than any 3d package for architectural type work or space planning.