Want to apply EE knowledge -- which microprocessor would you recommend?
Hey, great timing!  This week I've been interviewing E.E. students for an intern position.  Here's what I can say with 100% certainty:  Students from the big schools, even Juniors working on their Bachelors, have almost ZERO useful knowledge.  One guy I interviewed couldn't calculate the value for a current limiting resistor for an LED.  Yup, that's what $30k/year will get you for an education.   The point is, any practical experience or knowledge you have will put you above your classmates when it comes to landing a job!  Seriously, it's that bad out there.

Ok, on to your question.  From an employers perspective it doesn't matter which uC you use.  Odds are that whatever you choose, it'll be wrong.  What's more important is the experience and knowledge you gain will apply to most uC's.  That being said, stick to the common ones.

The Microchip PIC's are my least favorite.  The hardware is fine, but writing software for them is a super pain in the you-know-what.  I've used them in the past, and never again.  I've also used the Cypress pSoC 1.  It was nice at first, but their software is buggy and documentation is very lacking.  A current project of mine uses an MSP430, but it's too early to say how well it works.  The TI ARM based uC's are also nice, but might be too much for you at this early stage.