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Cyan comments on The Best Textbooks on Every Subject - Less Wrong
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Gelman's text is very specifically targeted at the kinds of problems he enjoys in sociology and politics, though. If you're interested in solving problems in that field or like it (highly complex unobservable mechanisms, large number of potential causes and covariates, sensible multiple groupings of observations, etc) then his book is great. If you're looking at problems more like in physics, then it won't help you at all and you're better off reading Jaynes'.
(Also recommended over Gelman's Applied Regression and Modeling if the above condition holds.)
Ah, interesting. I used the material I learned from that book in my thesis on data analysis for proteomics, so you can expand the list of topics to include biological data too; biology problems tend to fit your list of problem characteristics.