For most stuff I always go for supple, stiff where presentation is important is shit, really shit. Only time I really look for stiff as a property if using very heavy flies, 2" or above copper tubes or other heavily weighted stuff and I'm also interested in the abrasion resistance which such flies. That's as important.
I look at diameter first then the breaking strain. Breaking strain means absolutely nothing to me without diameter as this is the factor which determines how the fly will cast and fish.
That said, it's while since I looked at anything, I use one brand or fluorocarbon and one brand of copolymer that I have confidence in.
Cheers
Ben