Murray, yes, it does matter which way you go with the accidentals. In our equal-tempered world we tend to lose sight of the nuts and bolts of how scales are constructed. Or, too many people never get a clue. A# NOT = Bb.
In the case you mentioned (Mixolydian mode?) you wouldn't sharp the sixth to make the flatted seventh, because you are already using the sixth. Actually, to be correct that wouldn't even be an accidental, but rather the 'normal' note for that degree of the scale in that mode. But I am skating on thin pedantic ice and I'll stop.
And yes, Joe F, you would start a minor on la rather than clutter things up with accidentals to turn a major into its parallel minor.
Cheers
-Glenn