Don't start with organic chemistry or genetics unless you have a 5-year plan. Basic understanding of molecular biology (structure of DNA, central dogma, etc.) will be enough to get started. Finally, here is a book (1) that describes many algorithmic problems in bioinformatics that a techie could relate to.

[1] http://www.amazon.com/Introduction-Bioinformatics-Algorithms...

Coursera seems to have s course on Genome Science: https://www.coursera.org/course/genomescience

This is what you need: http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fj...

You have to start with organic chemistry and genetics. If you don't, you won't have a good understanding of what's going on.

Bioinformatics itself is huge, there are many many areas - protein folding, protein interaction, DNA/RNA interaction, all kinds of taxonomies, evolution, gene mapping, systems biology, etc etc etc.

I strongly suggest you pick something particular, because, otherwise, it's easy to waste years on learning many topics and not have any deep progress on anything in particular.