A basement slab always feels cold. If you want to make it a more cozy space, you might want to think about adding under floor heating.

It’s not just sub slab you have to worry about. Any stem walls all have to be insulated from the exterior too. Think of a house built inside a foam cooler. None of that house touched outside the cooler. Everything is behind foam. That is what needs to happen. The entire interior needs to be thermally broken from the exterior.

A thermally isolated basement slab will take the temperature of the surrounding space. If you consider 65-70 cold....

I suspect R10 will be enough but would recommend a little more in a cold climate with a shallow deep frost line.

Agree that you have to completely isolate the slab and walls from the cold of the outside - that can even include insulation UNDER the footings so that any poured concrete wall won't have direct ground contact.

Flooring material matters a lot of course. Whether a space feels warm is much more than subslab insulation. R 10 is generally fine.

insulation UNDER the footings

Only if the OP is attempting to meet Passivhaus standards.

Insulation is what keeps the slab at 70, and not a ground coupled 55. So insulation helps a great deal. But the floor will still feel cold to bare skin without a less conductive surface on top of it.

The reason a 70 degree concrete slab feels cold isn’t because of a lack of insulation. It has to do with thermal conductivity. It’s a large thermal mass that is cooler than your body, and it’s highly thermally conductive. It can quickly absorb the heat from your bare feet, away from your feet. Put wood over that concrete mass, and even a .5 R value, plus the lesser thermal conductivity, makes the floor feel “warm”.

Put wood over that concrete mass...

Or just wear socks!