Context. Exoplanetary properties strongly depend on stellar properties: to know the planet with accuracy and precision it is necessary to know the star as accurately and precisely as possible. Aims. Our immediate aim is to characterize in a homogeneous and accurate way a sample of 27 transiting planet-hosting stars observed within the Global Architecture of Planetary System program. For the wide visual binary XO-2, we considered both components (N: hosting a transiting planet; S: without a known transiting planet). Our final goal is to widely analyze the sample by deriving several stellar properties, abundances of many elements, kinematic parameters, and discuss them in the context of planetary formation. Methods. We determined the stellar parameters (effective temperature, surface gravity, rotational velocity) and abundances of 26 elements (Li, C, N, O, Na, Mg, Al, Si, S, Ca, Sc, Ti, V, Cr, Fe, Mn, Co, Ni, Cu, Zn, Y, Zr, Ba, La, Nd, Eu). Our study is based on high-resolution HARPS-N at TNG and FEROS at ESO spectra and uniform techniques. Depending on stellar parameters and chemical elements, we used line equivalent widths or spectral synthesis methods. We derived kinematic properties taking advantage of Gaia data and for the first time in exoplanet host stars we estimated ages using elemental ratios as chemical clocks. Results. The effective temperature of our stars is ~4400–6700 K, while the iron abundance [Fe/H] is within −0.3 and 0.4 dex. Lithium is present in seven stars. The [X/H] and [X/Fe] abundances versus [Fe/H] are consistent with the Galactic chemical evolution. The dependence of [X/Fe] with the condensation temperature is critically analyzed with respect to stellar and kinematic properties. All targets with measured C and O abundances show C/O < 0.8, compatible with Si present in rock-forming minerals. Mean C/O and [C/O] values are slightly lower than for the Sun. Most of targets show 1.0 < Mg/Si < 1.5, compatible with Mg distributed between olivine and pyroxene, and mean Mg/Si lower than for the Sun. HAT-P-26, the target hosting the lowest-mass planet, shows the highest Mg/Si ratio. From our chemodynamical analysis we find agreement between ages and position within the Galactic disk. Finally, we note a tendency for higher-density planets to be around metal-rich stars and hints of higher stellar abundances of some volatiles (e.g., O) for lower-mass planets. We cannot exclude that part of our results could be also related to the location of the stars within the Galactic disk. Conclusions. We try to trace the planetary migration scenario from the composition of the planets related to the chemical composition of the hosting stars. This kind of study will be useful for upcoming space mission data to get more insights into the formation-migration mechanisms.