If you are doing this to get a job, then the first thing I would do is inventory the job openings in your area (or wherever you want to live). While every metro area has jobs based on each technology, some areas have more jobs in specific technologies. I think the answers would vary quite a bit if you lived in Chicago vs. Boston for example.
I would also give some thought to what areas you would enjoy working in: web development, financial software, embedded software, games, mobile software, etc. These areas all focus on specific technologies and it is good to match them up.
That said, if you are looking for an entry-level position, a good hiring manager would agree with what others above have said. A solid understanding of fundamentals is most important and a good candidate can pick up the specific technology as they go. However, if you want to get through the resume filters, then it is good to have some experience in the technologies that the job posting requires.
A buddy of mine was very successful with this route. He wanted to switch careers, so he got a quick degree based on around COBOL programming. He’s had a job since he graduated. I should add that he graduated right around 2000, so I don’t know if Y2K gave him a boost.