Question: If I have a nice feature of digits in mind, how do I decide if I should include it into the set of variables I feed into my learning algorithm or not?
Answer: If you add a random variable, you don't improve the result, but you pay for it, because you increase the amount of variables. In each particular machine learning task you know the size of your data set and there is a way to determine the number of variables you can safely feed into the learning algorithm, we will be talking about it later.
In this case (digits classification) if you invent features by hand, chances are you will exhaust your imagination much earlier.
If you want to play with the digits classification data, you can find it at the bottom of the page
http://amlbook.com/support.html.
Lecture slides are available at
http://amlbook.com/slides/.