Hi Kevin,
I am a junior tech writer so I am probably not the most experienced person you can get advice from. However I did manage to get into tech writing, so maybe I can be of help.
I landed a job last year after completing an online course offered by the ISTC (the British equivalent of STC) and after writing some tutorials for a freeware software project. I had a small portfolio of 4 items, 2 of them written with OpenOffice, one with a wiki and one more with Scribus, a free desktop publishing software. This is to say that I do not think a perspective employer cares about what software you know: you are supposed to know how to write about technical topics, organize content, interview experts, edit, review... but it does not really matter what software you use. Ms Office, OpenOffice, or even simpler programs like AbiWord or a wiki are fine and cost nothing/very little. I know a very experienced tech writer who has worked for large multinationals for 25 years: he uses Word.
That said, even knowing Ms Word is less trivial than it sounds, and knowing it well can make you a better writer. You might want to google for some Word tutorials. And what I really recommend is writing for free: pick an open source project, or a charity near you, or ask a company or an organisation to work for free for a few days to build a small portfolio. That will show your employer that you are serious about writing, and you will have something to show.
idratherbewriting.com has a wonderful section for students: I read each and every article several times and used it as a source of inspiration.
If you want to know what tools and skills are most advantageous for TWs,
writersua.com has a yearly survey.
Cheers,
DiSc