Hello,

I personally would begin with print and move into handwriting.  I have found this link to be resourceful when I help my daughter with her horrible handwriting, one thing she has inherited from me.

It would be helpful to think about what is causing the terrible printing: Is it trouble remembering the letter formations? At age 10 that is probably not the case.  Have your son write all his upper and lower case letters with his eyes closed.  Those he hesitates on need practice.  If the letters look ok and actually may be better with his eyes closed than opened (less visual distractions), then you may need to look at his ability to spell, organize thoughts, capitalize, etc.  At times when there is a weakness in these higher level thinking skills, the brain tends to prioritize on that and the motor (legibility) falls apart.  There are 10 Handwriting Questions on lynslines.wordpress.com that could help you figure out which part of the whole writing process is contributing to his writing problem.  
As far as print versus cursive, once the letter formations are ingrained in the motor memory, its hard to change them.  So if he is comfortable with cursive, start there rather than trying to change poor printing habits. Computer use for long assignments may be an option.