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.
I am curious what you consider to be "very very cold". Here in Maine, 45 to 50 degrees at slab level 4 feet below grade is common. So interested in what temps you may have and the average relative humidity in that space.
With those questions asked; the straight answer to your question is yes, you should use a vapor barrier when installing any wood type floor over concrete. Both methods you mentioned would work. A one inch foam insulation, closed cell, waterproof, under the subfloor would be fine. If you use the tongue and grove style and fit it carefully, additional vapor barrier should not be needed. You can add a sheet of 6 mil plastic under the insulation for good measure if you feel the humidity is high in your area and are concerned with condensation. Another option is a paint on barrier such as Hydra-loc or any low pressure concrete coating used for interior waterproofing. Again, use this under your foamboard insulation. The one step method is the interlocking subfloor systems with a built in moisture barrier. this works well but is very pricey.
Best Answer
There is nothing wrong with putting engineered flooring on your slab in Florida. It can last a really long time and I have installed it in my own home on slab and helped with other homes.
Buy a really good wood. Make sure that you really give it a scratch test. Get samples and whatever. I used to take pennies, screwdrivers, smack my wife heals, all kinds of things on the samples. Let me tell you that most (80%) scratch easy.
Don't buy any engineered flooring that has mdf backing. Wood backing only.
The thicker the better. Don't let anyone talk you into flimsy engineered flooring, telling you thickness doesn't matter. IT DOES.
The underlayment... Normally I say rigid foam then 3/4" plywood then light flooring pad... But this is FLorida and you don't have the insulation issues. I would look for 1/2" rigid foam sheets but this depends on manufacturer.
I would wait 3-4 weeks for both house and wood in conditioned space.
I would also cut out the bottoms of the drywall so that you can use the drywall - probably 1/2" - as you expansion gap. This will allow you to use whatever trim you want without quarter round.
I wouldn't have the builder install any flooring. This will just cost you money and might hinder some of the engineered flooring installation.
Overall thoughts on engineered flooring on a slab in Florida vs tile or whatever... Obviously carpet is the easiest to do and the easiest to deal with. Tile though can have major issues. If your slab settles or cracks or whatever the tile will crack and have issues. The engineered flooring will handle smaller cracks without any issues. Major cracks, it depends.