From the companies I've worked in the main weapon of choice is CATIA v5, v 4 is used a lot, but is slowly being replaced with v.5 and the differences are so significant that you're better off with v.5.
I know you're looking at getting into CAD, but is desiging what you really want? or just a way into the offices? another option may be stressing. But that does depend on your qualifications.
The biggest problem you will face is a lot of places want so many years of experience on a system rather than a qualification in a system. Look at the larger manufacturers and see if you can get in on the ground floor as a designer then they will pay for all of your training. I know BAE are getting desperate for designers, maybe they would be a good starting point?
But the systems most commonally in use are:
CATIA v4 and v5
Pro-Engineer
Solidworks
and to a limited extent AutoCAD.