Discrete nickel catalyst nanoparticles (NP) have been used to grow isolated single-walled carbon nanotubes by chemical vapor deposition (CVD). Atomic force microscopy (AFM), transmission electron microscopy (TEM) and micro-Raman spectroscopy are used to characterize these as-grown, isolated nanotubes. Using a conventional setup, we are able to produce narrow diameter distribution single-walled carbon nanotubes (SWNTs) (1.45 +/- 0.5 nm), showing a clear mismatch with the larger broad size distribution of the catalyst nanoparticles (4.7 +/- 1.5 nm). Investigation of the growth conditions allowed us to synthesize, starting with the same catalyst materials, various carbon nanotube (CNT) samples with a wide range of characteristics. The advantages of such a versatile CVD method for the study of physical properties at the single nanotube level are illustrated by means of two prospective studies on SWNTs mechanical and vibrational properties.