I like designing (and have read a few typography books) but typography seemed like it was expensive to get into. What software do you use? What entry-level software is there?

For web and graphic design there was almost no monetary cost to learning.

For textual documents like academic work and literature LaTeX and its many packages are great for high quality typography. It has a steep learning curve though, but the results look professional and sharp if you follow the best practices. For things like beautiful tables and well-balanced paragraphs (i.e., the distribution and hyphenation of words) LaTeX is hard to beat. So if you are into typesetting books, that is a great option.

Nowadays there are plenty of good free fonts available too (although you are naturally limited). Free software fonts like Gentium are a pleasure on the eye in print.

I'm not too familiar with the more DTP side of software available as free software though.

Of course web browsers have come a long way too. Decent typography is already possible in the modern web browser, and more goodies become available all the time.

I've recently (within the past week or so) begun learning LaTeX for the purpose of typesetting my resume. It's actually been easier than I expected, and the result already looks much better than the Google-Docs-Exported-to-PDF that I had before.