Yes! Cleats are pretty much the standard in hardwood flooring. Typically, hardwood floors have 'tongue & groove' joints that interlock. First, some definitions of terms that I've used in my answer:
Tongue: the part that sticks out of the hardwood piece is called the 'tongue'.
Groove: the slot it fits into is the 'groove'.
Face: the part of the piece that will eventually be the floor is called the 'face'.
Floor joists: these are horizontal panels that run from one end of the room to the other and rest on beams under them. These provide support and you'll install the flooring on the joists, perpendicular to the direction in which they run.
CLEATS
With cleats, you drive the nail through the tongue onto the floor joists at a 45 degree angle. The cleats (which need to be set in) get hidden by the next piece that overlaps the previous one. The advantage is that all except the last piece in the room will have no nail markings on the surface.
The only con is that you'll need a specialized hardwood floor nailer, that can be pretty expensive to buy ($400-500 for a pneumatic one and $200-300 for a manual one). Needless to say, the pneumatic one is less work (but then again, you'll need to get a compressor for it) than the manual (you'll need a 5lbs mallet to drive a 1.5"-2" cleat in fully). However, these tools are easily available for hire at your local HomeDepot/Lowes (assuming you're in the US).
STAPLES
Now, I've never heard of anyone using staples for hardwood floors. It's more a carpet layer's tool. With staples, you'll also have to nail in through the face, thereby leaving marks all over the floor and ruining the appearance. You can probably use staples to lay down the backer board under the hardwood floor (if you're in a cold weather/windy area, this will help insulate the house by preventing airflow through the slots in the floorboard). Using them on hardwood floors is a terrible idea, and wouldn't recommend it under any circumstances.
The answer is "it depends" -- on what you need, on how well it's cared for, and how often you want to refinish it. Real wood is measured by something called the "Janka Hardness Scale" -- oak is a good choice, as it's rated at about 1300, with only more exotic woods being harder. I was told that Oak would probably be scratched by my dogs' claws, though, and I imagine that the invariable stones stuck in kids shoes will be worse. If it's possible, get real oak and make the kids take their grubby shoes off at the door... :-P
The "engineered" hardwoods are better because they're cheaper, but worse because they're not able to be sanded smooth and refinished. You'll usually see thicknesses plus a Janka measurement or an AC rating. The thinner the veneer, the more likely you are to crack through it no matter what the hardness of the veneer or the AC rating of the floor are.
For 100% composite stuff, such as Pergo and Kronotex, you'll see hardness measured on an "AC" scale that's basically a designation for how much traffic the wood is designed to bear in a residential or commercial setting. "AC2/Moderate Residential" will be too soft for your needs. "AC3 - Light Commercial/Heavy Residential" may be durable enough for your needs, but might show wear. "AC4/Moderate Commercial" is most likely what you'll need to go with, and it's harder to find and more expensive. However, it's less expensive than wood is no matter what.
Two things you didn't say... first, what kind of structure you're installing it on. Is it a wood subsurface, or is it slab-on-grade or slab basement? If it's on concrete in any way shape or form, you definitely want to go with something that is composite and less expensive. I know that you CAN install wood on slab-on-grade, but I would never consider doing it, personally. Second, what rooms is this going in? Wood floorings, regardless of composite or engineered or natural, is not good in places that will receive water on the surface or may be exposed to leaks. So the entry hall (front door and back), the kitchen, and the bathrooms are places to avoid having wood floors. I would keep vinyl or tile in those areas, or explore the wood-grain ceramics that are becoming quite popular for those areas or over slab-on-grade.
Best Answer
It looks like a typo for rows. Perhaps it was transcribed from a voice recording.