all species have different preferences. My house is a zoo. on top of my 14 reptiles 7 amphibians 2 fish tanks and all the mantises I breed my own food for them. I have 4 different species of roach colonies going, mealworms, fruit flies, house flies, firebrats and blue bottle fly cultures. I used to raise crickets, but roaches are far better and far less work. Most mantises will readily eat flying food. Some won't even look at stuff like roaches and crickets, even turn their noses at them, and a few species turn their nose at flying stuff and prefer low dwelling scurrying creatures.. When they are young they are typically fed fruit flies as they get bigger they move on to houseflies, and then blue bottle flies. They can hunt them all by themselves. If you want them to eat crickets and roaches, some species will hunt them, but others will ignore them. For these species you have to hand feed them by waving the bug in front of them with tweezers. Then there's the metallyticus. they are low to the ground and scurry around. They ignore anything that flies, they are pretty much built to hunt roaches on the barks of trees. Ironically enough though the biggest mantis species in the world can only eat fruit flies because their raptoral arms are soooo tiny.
as for flying prey it doesn't stop there. you can feed them wild caught moths, spiders, wasps, bees. any bug really as long as it's not poisonous. if it stings or bites I would remove the stinger or teeth first.
as far as individuals having certain preferences within their species, I believe it exists. I have two adult ghost mantises one won't even look at a roach or cricket. she only likes flies, while the other readily jumps at roaches.