It's always big dollar bill first, because if you give smaller dollar bills first at any point you'll always have potential oppotunity to run out of change for cases you can avoid getting into that situation.

Try thinking of a few scenarios and work it out in your head (or by pen and paper) ;-)

It's common sense in this kind of problems (even in real life), you'll always try to get rid of the higher value bills first, to not run out of the small ones.