I recommend Pattern Classification by Duda, Hart, and Stork. It's good because it is front-loaded with a lot of classical results on multivariate Gaussians, and discusses things like Fisher linear discriminant analysis, maximum likelihood, etc. The other sections of the book allow you to develop an understanding of how this connects with machine learning, which is important.
A lot of statistical texts do not make clear the overlap between classical statistics (e.g. likelihood models, logistic fitting, regression) and more modern machine learning (support vector machines, decision trees). While Duda et. al. is not a great encyclopedic source for all things statistics, I think it's a good first book. It's readable and bridges gaps, which is usually the early priority before needing to chase down lots of specifics to become an expert.
Another book that might be helpful in a similar way is: Data Analysis Using Regression and Multilevel/Hierarchical Models by Gelman and Hill.