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...

It's such a big area that it's hard to know where to start. Have you taken an intro class or something? That might be the best way to figure out what's out there.

I'm not sure what your computational background is but if you're not familiar with the basics like sequence alignment I suggest you check out a book. I'd recommend An Introduction to Bioinformatics Algorithms by Neil C. Jones (http://www.amazon.com/Introduction-Bioinformatics-Algorithms...). In addition to describing the algorithmic techniques, it gives synopses of current research issues and big names in the field. There are also hundreds of sample problems - some of which are active research problems - and no answer key (because often these types of problems don't have clear "best" answers). It's kind of like being taught how to swim by being thrown in a lake. If you survive, you're better off for it.

Also, before approaching professors it helps to have read and understand their description of their research interests and maybe have read a few of their recent papers. This will give you an idea of whether they're doing something that you might be interested in or not.