Quickly I see that the 1.33mm is labeled Cell Height whereas the cfd-online calculator give center of cell distance, so there seems no discrepancy there… 1st layer thickness = 2 times cell center distance…
As far as tutorial values, you would have to show us where it is derived…
Yes it is worth getting it right… (I suggest aiming for y+50 to get a wall function mesh, then, if needed, tweek after you see a y+ surface mapping from a converged sim run)