Machine learning algorithms: which algorithm for which issue?
Take Andrew Ng's machine learning course on coursera. It's beautifully put together, explains the differences between different types of ML algorithm, gives advice on when to use each algorithm, and contains material useful for practioners as well as maths if you want it. I'm in the process of learning machine learning myself and this has been by far the most useful resource.
(Another piece of advice you might find useful is to consider learning python. This is based on a mistake I made of not starting to learn python at an earlier stage and ruling out the many books, web pages, sdks, etc that are python based. As it turns out, python is pretty easy to pick up, and from my own personal observations at least, widely used in the machine learning and data science communities.)
It is very hard answer the question “which algorithm for which issue?”
That ability comes with a lot of experience and knowledge. So I suggest, you should read few good books about machine learning. Probably, following book would be a good starting point.
Machine Learning: A Probabilistic Perspective
Once you have some knowledge about machine learning, you can work on couple of simple machine learning problems. Iris flower dataset is a good starting point. It consists of several features belonging to three types of Iris species. Initially develop a simple machine learning model (such as Logistic Regression) to classify Iris species and gradually you could move to more advanced models such as Neural Networks.
@TooTone: In my opinion Machine Learning in Action could help the OP with deciding on which technique to use for a particular problem, as the book gives a clear classification of the different ML algorithms and pros, cons, and "works with" for each of them. I do agree the code is somewhat hard to read, especially for people not used to matrix operations. There is years of research condensed into a 10 line Python program, so be prepared that understanding it will take a day (for me at least).
scikit-learn.org published this infographic, that can be helpful, even when you're not using sklearn library.