Hey there,
My godmother's daughter had a baby recently and they had to purchase a new apartment. Now, they were faced with the same choice you are - they had a brand new flat, but the flooring consisted of laid down tiles, so they had to renovate. Since tiles would be really cold 'till they warm up in the winter, and the toddler could have gotten ill because of that.
As far as I know, they chose a laminate flooring with a scratch protective layer. I thiiiink they bought one of these, but I'm not sure -
https://www.flooringsuppliescentre.co.u ... index.html .
They decided that the easy to maintain floor with the look and feel of real wood will be a good idea to go along with the little rascal.
As for the linoleum, it will have to be laid on top of a concrete floor, so it's going to be both hard and cold