I used 3/4" screws(don't remember the size)( big enough to fit flush in the holes in the metal base), and drilled a small pilot hole 1/2" deep, just enough to get the screw going in the correct direction.
The thickness of the carpet and the metal base will easily take up the other 1/4" inch.
You just don't want the screw going thru the 3/4" plywood floor. If that happens, you'll have the screw dragging on the main floor under the slide floor. You don't want that!
I mounted the bases on the tabletop first, inserted the legs, and positioned the "table" where I wanted it to sit.
Measured the bottom bases to be the same width from each side of the dinette walls.
Drilled the pilot holes.
Used the drill to screw the screws in tight.