I went the academic route into Bioinformatics - BSc in Biochemistry, then a PhD in Molecular Neurobiology. The fields of Bioinformatics that I'm familiar with are DNA/protein sequence analysis, expression analysis, genome and genetic analysis, protein protein interactions/pathway analysis and 3D structure analysis. I have been using bioinformatics since 1988 so I was lucky enough to be in before bioinformatics was thought of as a buzz word.

After 7 years of postdocing I found a job with a reasonably well known bioinforamtics company that produces both desktop and enterprise level bioinformatics software. To do all that I had to pick up a lot of Maths, a reasonable amount of Perl and skills in *nix, relational databases and diverse other computer/techie things

Finding folk with these skills sets is not easy. Most of my hires have a Batchelors and a Masters, PhD or Masters and PhD combination. The main reason for the heavy educational background is that to be a competent bioinformaticist, you need to have the experience in doing the biology as well as the computers - this takes time. I also tend to look for actual real projects, eg show me your source code/database schemas, where are your papers, etc. For me this is the main way to screen out folk who can do it, not just talk about it. You might look into certification programs - the best one that I know of is in Montreal - the Canadian Bioinforamtics certification program http://www.bioinformatics.ca/. It has an excellent combo of hands on training and theoretical background that you will need to pursue bioinformatics usefully. Otherwise pick a course that allows you to carry out projects that have real goals/results and hopefully publish papers. This is really the best way of getting your foot in the door for this field.

I am thinking of taking a Masters in Maths at this point - I find this a lot more interesting and difficult than doing a Masters in Computers/IT, but that is my personal bias. Part of that bias is that I'm not too impressed with the product of many 2 year Masters level IT programs in Colorado - they are rather too cooky cutterish and produce folk with some knowledge, a lot of not very grounded opinions and little practical application in tackling real problems. A Maths degree is (hopefully) less popular so I hope it will be a bit more applicable to my current needs.

If you want a starting reading list, try the following:
Biological Sequence Analysis Durbin, Eddy, Krogh, Mitchison excellent introduction
Computational Molecular Biology Pevzner - the first text book on bioinfo algorithms
Bioinformatics the Machine Learning approach Baldi Brunak - neural networks and machine learning
Molecular Modelling Leach - 3D structure analysis, the sexy topic of the first decade of the new millenium
Computational Analysis of Biochemical Systems Voit - actually a more difficult and interesting probem to my mind
Information theory and Molecular Biology Yockey - an alternative view of informatics that doesn't rely on neural networks and hidden markov models
Bioinformatics Sequence and Genome Analysis Mount - pretty good but expensive text book
Society of Mind Minskiy - not strictly bioinformatics but it does have interesting ideas on the mind which I tend to look at as issues of bioinformatics, again a personal bias.
Analysis of Human Genetic Linkage Ott - the book on genetic linkage analysis. Combine it with Liklihood by Edwards or the Calculation of Genetic Risk by Bridge and you can cover both simple inherited diseases and complex non-mendelian inherited diseases.

Good luck.

Update Two other titles that might be entertaining:
Algorithms on strings, trees and sequences Gusfiled - probably the text book on string manipulation and pattern matching problems, this one may be of general interest to most Monks
Time Warps, String Edits and Macromolecules: The theory and practice of sequence comparisson Sankoff and Kruskal - this one is the ur-textbook on sequence comparisson, agin it may bge of general interest to Monks. MadraghRua
yet another biologist hacking perl....

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