Predicting next medical condition from past conditions in claims data
I've never worked with medical data, but from general reasoning I'd say that relations between variables in healthcare are pretty complicated. Different models, such as random forests, regression, etc. could capture only part of relations and ignore others. In such circumstances it makes sense to use general statistical exploration and modelling. 

For example, the very first thing I would do is finding out correlations between possible precursor conditions and diagnoses. E.g. in what percent of cases chronic kidney disease was preceded by long flu? If it is high, it doesn't always mean causality, but gives pretty good food for thought and helps to better understand relations between different conditions. 

Another important step is data visualisation. Does CKD happens in males more often than in females? What about their place of residence? What is distribution of CKD cases by age? It's hard to grasp large dataset as a set of numbers, plotting them out makes it much easier. 

When you have an idea of what's going on, perform hypothesis testing to check your assumption. If you reject null hypothesis (basic assumption) in favour of alternative one, congratulations, you've made "something real". 

Finally, when you have a good understanding of your data, try to create complete model. It may be something general like PGM (e.g. manually-crafted Bayesian network), or something more specific like linear regression or SVM, or anything. But in any way you will already know how this model corresponds to your data and how you can measure its efficiency. 



As a good starting resource for learning statistical approach I would recommend Intro to Statistics course by Sebastian Thrun. While it's pretty basic and doesn't include advanced topics, it describes most important concepts and gives systematic understanding of probability theory and statistics.