I liked "Hands on Machine Learning" by A. Geron. It's quite practical - you won't find careful progressive proofs, but it is very good at introducing the methods of ML and relating them to real problems. It provides you with a way to get your hands round the techniques - with an MSc in Stats you should then be well placed to understand where the gaps and problems are and to use things wisely.

It isn't quite state of the art, and it is very light in terms of how to evaluate and deliver the solutions. But I thought it was good. My team at work has gone through it selecting one chapter at a time this year in our book club - it's provided a good catch up and share forum for us. Some of the folks in the team are Engineers and so haven't a strong ML background, a couple are Data Scientists and therefore were in the same place as you (+/- some use of deep learning in a few engagements) and a couple of the folks are diehard ML researchers, but focused on different things (time series, NLP, evaluation) so there was a lot of crossover for everyone.