I decided to go for engineered flooring in my last house, very easy to
put down. It was a 3.6 mm veneer and wasn't any cheaper than solid wood
but I thought it was likely to be more stable over concrete. I reckon
2mm would be fine if you don't intend to do too much agressive
refinishing.

How flat are your concrete floors? In the lounge I had to rescreed the
floor to get it flat as there were dips of up to 1.5 inches!!!, I
hadn't noticed the dips when it was carpet but a wooden floor is going
to be a bit bouncy if it is not supported. Something to bear in mind.

Geoff