Chun pretty much hit the nail on the head, from my experience.
I got started with mantis' by indoor gardening, but the pests are not large enough to interest the mantis, unless you have beetles and roaches messing with your garden.
I think the first you'd go with lacewings. The larva eat the small parasites for a couple weeks, then they mature into the lacewing adults and leave, or hang out if there is pollen and honey for them to eat, and I was told, but didn't witness, that the mantis' will eat the lacewing adults.
The ladybugs are good for eating stuff, but they don't care for spidermites, which can be the worse enemy of an indoor garden. The lacewings will eat the mites, but if you put lady bugs in before the lacewings, they may eat the lacewing larva, or maybe not. So I'd stage the lacewing larva first, then the ladybugs, and mantis'.
The mantis' will not eat the lady bugs, at least not the your mantids. They may eat them if they are adult mantids, but I don't know. Some say the ladybugs repel mantids, I don't know.
I'd say lacewings for the whiteflies though.
I think I'd stage them, if you get lacewing eggs, in one week hatchings. That way you'll have larva eating the mites and whiteflies. Then do the lady bugs after a month or so, then more stages after they all leave.
If you have bad spidermites I'd say to spring for predatory mites, as they'll clean them up. You do need to get the correct predatory mites for the humidity level and temperature though. They usually recommend two kinds, as some predatory mites leave as soon as they get hungry when the prey thins out, and a different species may stay long to control and lingering stay mites.
I could say to use pyrethrum , but that would affect any biological control that you're trying to use, in a negative way.
I don't recommend pyrethrum unless there is a major overun of predators that can't be controlled by the beneficial insects, but you won't be able to introduce beneficial insects for some time after that application, or you'll kill them also.
Diatomatious earth is an organic pest control, but it may kill your mantis' if you use it, as it'll cut them up and cause fluid loss, and death possibly.
Just do some research online, and stage your predators correctly, or they'll just kill each other off, and you'll gain no benefit.
Soapy water will kill alot of insects, by smothering them.
In colder climates the pests don't grow as fast, plus you can use a carbon dioxide generator to increase growth rate, and some do this so the garden is grown before pests get a good foothold.
As to mantis' hatching in the garden
I hatched some in my indoor garden and I wasn't aware they needed humidity, and they dried up and died, so you will have to keep conditions up for the young nymphs, or they die.
They won't be able to catch prey as easily since the prey won't be contained in a small area that they can get to easily. They'll probably start eating each other at that point, or starve.
I decided to raise the nymphs first, to close to adult size, then start the garden, so the mantis' will be ready to live on their own, and be able to get around well enough to catch prey.
The green lacewings were affordable, and locally available, so that's what I used for mites and other small pests. I then used lady bugs. You'll need to do some 'maintenance' or the mites and other pests may start back up later, and once they get going they roll pretty fast.
They say to take the plants outside and spray the bad bugs off first, then bring the plants back inside and put your biological controls in place. It'll reduce their workload tremendously, and help eradicate the pest much faster.
You'll want to release the beneficials after watering the garden, or whatever if you're using hydroponics. Google it. The water keeps the insects from running off, somehow... hmm
Google beneficial insects, but do keep in mind that some beneficial predators will counteract the other beneficials if not staged correctly.
Some of my tomatoes were excellent 
My dad argues with me when I try to take some to my apartment He wants them for himself cause they taste so much better than store bought.
I will say I didn't get the kind of production that I expected. Not even close, but the quality was worth the effort.
I'd get bell peppers starting to go, then the insects would attack them and I'd get no peppers, but the tomatoes were tasty, and meaty
I prefer beneficials over pesticides, even if the pesticides are organic.
BTW you can use other plants to draw bugs away from your food plants, if they are more attractive to the pests. Marigolds will draw spidermites. Other types draw other pests. Try googling beneficial or companion planting, and keep in mind, some plants repel certain pests, but also attract possible worse pests, so research well
