I tend to be a gear obsessive kind of person, and so I go with the approach that carrying as little as possible is preferable and looks best, but when I have to carry something, I get picky about what it will be.
For work, I had some really cool messenger bags - my first one was a nicel looking all leather that was distressed to look masculine and a bit dated. Later, after the flight jacket kind of look went out, I got one that was a bike messenger bag of some tech fabric that looked sleek.
For running the dog when i have to carry the dog's stuff, I use a very small hydration backpack with the bladder stripped out. It suits the purpose and looks appropriate for running. And I also outfit the special dog running belt with a couple of specialized pouches for treats and poop bags - very streamlined.
Nowadays about all my shorts and tights have zipper pockets so I don't lose crap.
For running club sessions, I have a Puma backpack that has a sports ambiance.
For gym workouts where I need the jump rope, leg weights, etc., I have a little construction bag that's easy to use and might be a little dorky, but gets the job done.
Other than that, I wouldn't be carrying things.
tl/dr - use a bag/carrier appropriate for the activity.