What is a simple image classification ANN architecture and a simple data set? I'm looking for a neural network architecture, which gives pretty good performance on an image classification challenge and is still simple to implement in a framework and also reasonably fast to train. Do you have suggestions?

I'm new the neural network implementation, and in the end, I'd like to do some "research-style" playing with it.

Moreover, a pointer to an image classification data set which is not too tough for a simple network would be great. However, not something like MNIST which is so easy that almost any classifier does a good job.

PS: Which neural network framework do you recommend if I'd like to modify the way the network is trained?
I'd advice going through cs231n course, which covers this.

A simple but good architecture is using a feed forward net with one hidden layer and ReLU.

As for dataset - CIFAR-10 is good, if you don't like MNIST.

Tensorflow is quite easy to use framework.