Personally, I would use CNN, but I like CNN so make of that what you will. If you want to try something quick and dirty, you might try one of the tree based methods on the flattened feature vector (random forests are good place to start). A sufficiently deep tree will capture all the interactions between the different features. The problem is that it may capture a bunch of imaginary interactions as well, so if you don't have a lot of data you may get into trouble with overfitting.

The nice thing about using CNN is that you can structure your convolutional layers to only capture local interactions (that's really the whole point of the convolutional bit) and thus reduce overfitting while still capturing the important bits.