Concrete wicks up water from the soil so there is need of a vapor barrier no matter how dry the climate. Even plywood shouldn't be put directly onto concrete, unless it's dampproofed.
If
1. the concrete floor has been poured over a layer of crushed rock or coarse gravel that has been topped with impermeable plastic or roll roofing,
2. since as you say the climate is dry,
and
3. if the site provides drainage away from the house for times when it is wet, and
4. if the top of the slab is at least about 6 " above grade,
one of those concrete sealer paints might be enough. You could probably lay the wooden floor right over that.
You'll need to use a resilient underlay if you use strip wood (tongue and groove). This is to provide a level base for the narrow strips. If that underlay is waterproof, it would kill both birds.
I once saw a very weird but very cheap idea for wood flooring on a television program but I never actually tried it. This guy cut 4" x 4" posts into one-inch thick 'tiles' (that's right, each tile was 4" x 4" x 1") and sanded them one side and glued them down and then stained them. This was labor-intensive but practically free, because he used recycled wooden posts.
They looked great.
The reason I think of that is that cut that way, the grain would run perpendicular to the concrete sub-floor. This would allow moisture to 'wick up' through the wood and evaporate. I suppose you should use non-waterproof glue or grout, and stain, not varnish.
When we built our house my husband let me make all the decisions because, quite frankly, he didn't want to move to the country. (He loves it now.) Then, he hoped I'd get discouraged and give up the idea. Anyhow, the one condition he made was that I not exceed our cash resources - in other words, no mortgage.
So we had over-runs on the septic system and the well, and so I had no budget for flooring.
So I painted the plywood (it was good-one-side, luckily) after doing some minor filling and sanding, and a scrupulous scrubbing. I used a 'diamond' (hard finish) water-based paint, three colors, and sponged it on. The sponged pattern helped conceal that it was 4x8 panels, imperfectly sanded!

When we moved in, the house was not completed yet, I took this photo:
Moving-in day.(Pardon the glare from the sunlight on the floor. The colors were actually uniform in depth.)
It did just fine until I had saved enough to do a proper floor, two years later. In fact, my neighbor said it was a shame to cover it! It was also very easy to keep clean because the paint was so hard.