You can do what we did for our dog. Make a list of the qualities you want in the cat first. Like color, male/female, short/long hair, younger (kitten)/older., purebred or purebred looking, etc.
That way you can eliminate those you know you don't want. For example, when we picked out our dog we had a list of:
Light or white color
Female, preferably spayed
Medium - no more then about 60-65 lbs
Lab or lab x
House trained/obedienced trained
Keno fit the bill almost 100% - she was not spayed at the time, but we paid for that.
For cats, I would chose short over long hair - I don't have the patience/time to groom a longhair cat every day
. So if I was looking for a cat, I'd pass up the longhairs and move to the next. I also like calicos and red or brown tabbies over some of the other colors. Again, if it was not on my list as "ideal" - I'd keep looking.
If you don't have a list made up of the basics you both want in a cat, you'll have a tougher time picking one out and EVERY cat will be "cute/adorable"....
Good luck in picking the right cat for your family