For the top and legs ash, oak, cherry, beech and maple are all suitable (top about 250-300mm in diameter and about 35-50mm thick, legs about 250-350mm long).
If one side of the blank is level and smooth then this can be attached to a faceplate or screw chuck as this will be the underside of the seat. If the blank is rough or cupped then I fix this to a small disk with a hot glue gun. I always prepare this disc with a dovetail recess before gluing. The secret of this method is not to spread the hot glue all over the disc but to put 4 or 5 blobs near the edge of the disc (the glue stays hot longer).
Now turn the blank to its size and shape. The centre third of the top is slightly dished, as it is more comfortable. The top could have an inlay in a contrasting wood or a feature burr. If you are into pyrography this is a creative option, too.
Drilling the Holes
If you used a thinner disc than I mentioned earlier then the holes would have to go all the way through and be glued and wedged. I shall mention a few ways to get the leg angle correct. This I have found to be about 15 degrees off the vertical. Set a compass to the radius, then mark 6 points on the back of the disc, alternates will space the legs out accurately. I use a saw tooth drill bit.
Using a pillar drill you can set the angle by adjusting the table then clamp the disc to the table. Remember to set the depth stop carefully.
It is possible to use the lathe. This requires a jig to be made to slide on the lathe bed with an angled piece to clamp the disc. Then you would use the tailstock to push the blank into the drill.
The last option is to drill freehand with an electric drill. After all, that’s how it was done in the past with a brace. I would use a block clamped to the blank which has the correct angle for me as a guide to follow. Tape on the drill bit would be the depth guide.
Turn the leg to a cylinder, then use calipers to turn the tenon to its size. Take time here as it needs to be a close fit but still allow excess glue and air to escape. The rest is basic spindle turning with beads, coves and long curves. The design is really up to you. Now make two more exactly the same to match.