The problem with any underfloor heating is to ensure it does not get too hot, around 29°C is limit, so with wet they limit the water temperature with special manifold, with electric either sensors in the floor or use a special cable which as it gets hot its resistance increases so it is to an extent self regulating. The other problem with electric is in some areas you need to have earthed mats or braid to ensure no one can get a shock, and when I fitted it could not get self regulating type which could be used in a bathroom, that may have changed now.
First job was dig up the floor, OK in my case had to be dug up anyway to access drains, but installing at least 2" of insulation below the heating mat can work out expensive. Yes if floor already insulated you can fit a rather thin type directly on existing floor, but most floors are not already insulated, so it's a dig up the floors job.
When I have looked at buying houses I have found it is hard to find evidence that insulation has been laid, it seems the inspectors had same problem and the houses as a result had a very low energy rating, I actually rejected houses as shown as G the lowest rating, and did not know why so low, so would not take the chance. I would assume as with doors and windows where the installer must issue a certificate to shown done correctly, you will need the same with underfloor heating, be it pictures of the installation going in or a certificate you will need to show the guy doing energy rating that is was done correctly.
To be frank our under floor heating is only used to dry floor of wet room, it does not heat the room all it does is remove chill off the tiles, if using carpet or wood on the floors it would be a waste of money, and although I have bare tiles in wet room I don't have them anywhere else that can be seen, I know hall has beautiful tiles, but prefer to have carpet.
So selecting does depend on the room, the kitchen in this house has quarry tiles and they were laid so the solid fuel stove could be raked out without damage to floor, however it is rather unforgiving if you drop anything, I prefer a carpet so if I drop a cup there is a chance it will survive. If I wanted a heater not taking up wall space I would use a Myson kick space heater which would warm floor anyway.