For an EE learn ASM then C .
The reason why is almost all hardware for EE work, ARM, Mips, Pic, 8051 , are based in ASM and C/C++ . These are not devices with large amounts of storage and often you have to fit the program code in 1MB of space or less. You also need direct control of the functions without anything else getting in the way.
With embedded devices it is like a pc with a usb stick with 1MB storage as the only way to run software. There is no OS on these devices 95% of the time ( no room) and your program is the only thing running . If you want to do something like multithreading it is often done with interrupts that you set up. There is no memory management, you have write that code or maybe there is a dev kit that helps with that if you are lucky. It is a blank slate with a bunch of registers. If you are lucky you have some libraries to do different functions and add support for interfaces and things like sensors. If not you have to write those too. If the platform has enough ram and storage then they usually run linux. So that is something else you can focus on if you don't know it already.
Put that you know ASM on a resume and you will get noticed by employers because they know if you know ASM then you know how the hardware works and not just how to write code and hope the compiler gets everything right.
If it were me I would start looking at ARM devices. ARM is upcoming and soon to be huge . Intel is said to possibly lost the net book market to them later this year. And the cost to get started learning it is really low. The cost to try it out is zero.
Get qemu that emulates the processor . And you can get started writing code for lots of embedded devices for free to see what you like best.
http://homepage3.nifty.com/takeda-toshiya/qemu/