Using higher subsurface modifier values I found this nice playlist of general tips. Particularly I am interested in the first video.

You can clearly see, at about 1:50 that the author is using a value of five in his subsurface modifier. I can only go as up as 6 though, and as a result my shape is not that much smooth.





Is it something on my end, and if yes, how can I make this shape completely smooth?
Yes, you can use higher subsurf levels by typing the values directly, rather than using the slider.
See How can I set sliders to values outside the limits allowed by their slider?

However in this case it looks like the bumpiness is more likely to have been caused by something like this:
Weird deformation between large ngon and edge ring
To fix it, try adding some supporting geometry.