Fischer-Tropsch catalyst preparation parameters, such as cobalt precursor and impregnation solvent, determine structure and in fine catalytic performances of Co-based catalysts. Co particles of 3-7 nm mean size were prepared by incipient wetness impregnation on surface-oxidized CNT. In this work the crucial impact of the chemistry operating between the Co precursor and the support during catalyst preparation on the catalyst properties is demonstrated and the influence of CNT surface chemistry on catalyst characteristics has been assessed. Very good correlations were found between: i) the reduction degree of the catalysts and the concentration of the Co(OOC-) surface species; ii) the Cohcp/Cofcc ratio and the amount of CO-releasing groups on the support surface; iii) the extent of hydrogen spillover and the concentration of quinone surface groups. The initial catalytic activity could only be correlated to a combination of catalyst features: percentage of Cohcp, Co confinement, hydrogen spillover, and surprisingly the inverse of the Co initial particle size. No significant differences in SC5+ selectivity were observed, in accordance with comparable final Co particle size. Finally, the stability of the catalyst can be correlated with the initial Co particle size and the percentage of Cohcp in the catalyst. These results confirm the significant impact of the precursor/support couple on the structure and performance of Co/CNT catalysts, and reveal for the first time an inverse correlation between Co particle size and activity, which is attributed to the confined Cohcp phase.