On-line character recognition is a challenging problem. Much of the difficulty stems from the fact that pattern recognition is a complex process that cannot be solved completely by analytical methods.
Sending the order could cause the NN a lot "smarter", but if you're just learning, try the bitmap version first and see how well it works. Also, play with the bitmap granularity. Possibly you can try digit recognition first, there are standard datasets for that problem on the web. Not only you need to send the X/Y coordinates, but also the ORDER they were drawn in. So a path might be beneficial than just a set of points. A neural net should be able to manage it, and there are many ways it could. One way might be to divide up the path in n segments for n neurons and have each neuron recognize a piece of the letter.
If you wish to learn about Neural Network visit this Neural Network Tutorial.