So just to clarify terms up front, computer science is primarily about software (though it can touch on hardware aspects, e.g., quantum computing), while computer engineering is more about hardware (though you can do nothing but [embedded] software with such a degree--generally tied very closely to a particular type of hardware). There's a gray area there, but those are the definitions I'll assume.
I currently work as a software engineer, which is what computer science graduates tend to end up doing. I've been doing it for around 15 years now, and I like it a lot. (I also worked in the semiconductor industry for a while, and there were probably computer engineers there--certainly there were people who designed chips--but I worked with software people: video codecs, board-support packages [the lowest-level software to make a chip usable by customers], and in my case, embedded Linux and VxWorks. I wasn't as fond of that, though it had its good parts, too.)
For the more hardware-oriented folks, Raspberry Pi is probably the most popular embedded platform in the world (not counting mobile phones, which give you almost no ability to modify the hardware), and it's both cheap ($35 to $50, I think) and has a huge community of enthusiasts doing all sorts of interesting things with the platform.
And once you get to college, internships are an outstanding way to get your foot in the door, as you've already heard. But working on projects like those above can be just as good; it shows you're self-motivated, interested, able to work with the community (hopefully :-) ), and already have some experience with the engineering/development process: writing code, getting it reviewed, submitting it, etc.
As to specific jobs, there are countless Internet and software-only companies, of course (Silicon Valley is composed of almost nothing but), but almost every medium to large company these days has a lot of data and a need to manage it, slice and dice it, derive business insights from it, etc. On the transportation front, both gas and electric vehicles and (electric) drones are not only full of electronics (and the software that runs on it) but increasingly robotics in the form of self-driving (or self-navigating), autonomous vehicles. Tesla's "autopilot" woes notwithstanding, this is unquestionably the wave of the future, but it's also quite complex (probably obvious :-) ) and will require a great deal of refinement, debugging, and associated support infrastructure in the future. And then there are the scientific fields (physics/astrophysics, genomics, etc.) that will soon be generating terabytes or petabytes of data every day; while these fields may not pay particularly well, they have a huge need for big-data analysis and machine learning capabilities, and in some respects people working there will be at the forefront of engineering (and science), which can be its own reward.