The good part is that website has images with the chair from several angles. This will be extremely helpful.

What I suggest is to use Artisan for this job. You can do a very simple proxy, low poly, few segments and then subdivide the parts in order to get the smooth appearance.

Just be careful to have the subdivisions as even as possible (don't use very elongated triangles or quads if possible) and you will notice there are several "good techniques" in order to get what you want with artisan. Part science, part art.
Look to other artisan models here on the forum.

Good luck.