I frequently fly with my dogs, so my carrier may need to be a little more comfortable then most but here are the rules I follow:
I like mine to be able to stand up and turn around in their carrier.
PLENTY of ventilation- if it is a hot day you want plenty of air getting in so they can breathe.
A sturdy bottom so the bag stands up on its own and doesn't flop over and when carried the dog doesn't sag.
Comfortable arm loops so my shoulder isn't killing me by the end of the day.
Room inside for a small carrier blanket and maybe even a toy.
Side pockets of some kind to fit a wee wee pad, a small bag of kibble, a leash, and some wipes.
The bag must enclose all the way around with zippers, even if has an area that just snaps shut or doesnt really shut at all, my dogs WILL get out.
If the bag has zipper locks that is even better because mine have been known to unzip things.
I like the mesh area to be made with as high quality mesh as possible because mine will chew.
Here is a bag that fits ALL my criteria that I am considering ordering even though I have like a MILLION carriers already:
Sturdi Products Incognito Pet Carriers