For handwritten character recognition you need
- many training examples (maybe you should create distortions of your training set)
- softmax activation function in the output layer
- cross entropy error function
- training with stochastic gradient descent
- a bias in each layer
A good test problem is the handwritten digit data set MNIST. Here are papers that successfully applied neural networks on this data set:
Y. LeCun, L. Bottou, Y. Bengio and P. Haffner: Gradient-Based Learning Applied to Document Recognition, http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf
Dan Claudiu Ciresan, Ueli Meier, Luca Maria Gambardella, Juergen Schmidhuber: Deep Big Simple Neural Nets Excel on Handwritten Digit Recognition, http://arxiv.org/abs/1003.0358
I trained an MLP with 784-200-50-10 architecture and got >96% accuracy on the test set.