This is a common 2-plank chair. Any common 2x12 plank from the lumber yard will work. A wider plank helps a little with comfort, but is not necessary. Finding wider than 12 inches gets iffy and pricey. 2x14 can be found, 2x16 and wider are almost special order from a sawmill.
After kiln drying, that 2x12 is generally 1 1/2 by 11 1/2 inches. So the size is very close to the metric dimensions you stated. Type of wood also affects price and availability. The pine type woods are fairly common. Walnut would offer similar weight with better strength and look - but cost would rise dramatically. Watch for straight grain and few knots when picking out your board.
So any lumberyard should carry them as a standard dimension board.
I see a lot of these 2-plank chairs at the living history events around here. They work well, and look "primitive", but are mainly an early 1900's style of chair.
Setting them at a true 90 degree angle does sit OK, but you have to keep the lower leg higher and/or the back leg shorter to be comfortable. Increasing the angle a little helps in comfort, and allows you to sit a little closer to the ground. But they are still tippy to the sides.
You can nail up a similar chair out of smaller pieces of wood - like 4 pieces of 2x4 the length you need, and a couple pieces of plywood to work as your seat and back rest. Just have the "seat" portion slide through a slot in the "backrest" portion. Nail a short section of 2x4 across the front bottom side of your backrest at the height you want above the ground, and another piece on the back at the right height to brace against the seat portion at the height/angle you want. You are nailing up that "slot" for the seat portion to slide through the backrest portion. Short lengths of 1x4, 1x6, etc. can be nailed across for the seat and backrest instead of plywood, and you can space them out with a little gap between each board for that "slatted" look. A 2-piece chair nailed up like this weighs a lot less than a full 2-plank chair.
Just some things to consider. Have fun playing with it.
Mikey - out in the Hinterlands