I am interested in applying statistics/machine learning to the field of finance

I have a very strong background in finance, but much weaker background in statistics and computer science. I am interesting in learning this topic to apply to my work in financial research.

To be more specific, I am interested in using historical data about a company (company 10K, for example, which includes income statement, balance sheet, etc), and from this data predict their credit rating (which is given by a third party. There are a number of academic articles written on the topic that suggest high accuracy. However, these articles obviously aren't aimed at someone just exploring the field.

So where do I begin? If i wanted to accomplish something like this and get my feet wet, what software do I need? what books/references should I have to learn more? Avoiding returning to school, what are some of the basic books I should read if any (such as linear algebra).

Thanks for your comments.