If you have the Statistics and Machine Learning Toolbox, the easiest way to get you started is to run several classifiers with the Classification Learner App. QDA or SVM might be good options but it's hard to tell because it very much depends on your data.
As a side note, it may be that some of your examples "belong" to both class 0 and class 1 to some extent, in which case you may want to reflect this degree of membership with things like fuzzy c-means clustering.
If your features really overlap too much, a possible solution would be to work with a "raw" representation of the data (e.g. an image, no explicit feature) and let a neural network (like a CNN) extract relevant features for you.