The ²²Ne(p,γ)²³Na reaction takes part in the neon-sodium cycle of hydrogen burning. This cycle is active in asymptotic giant branch stars as well as in novae and contributes to the nucleosythesis of neon and sodium isotopes. In order to reduce the uncertainties in the predicted nucleosynthesis yields, new experimental efforts to measure the ²²Ne(p,γ)²³Na cross section directly at the astrophysically relevant energies are needed. In the present work, a feasibility study for a ²²Ne(p,γ)²³Na experiment at the Laboratory for Underground Nuclear Astrophysics (LUNA) 400 kV accelerator deep underground in the Gran Sasso laboratory, Italy, is reported. The ion-beam-induced γ-ray background has been studied. The feasibility study led to the first observation of the E _p=186 keV resonance in a direct experiment. An experimental lower limit of 0.12 × 10⁻⁶ eV has been obtained for the resonance strength. Informed by the feasibility study, a dedicated experimental setup for the ²²Ne(p,γ)²³Na experiment has been developed. The new setup has been characterized by a study of the temperature and pressure profiles. The beam heating effect that reduces the effective neon gas density due to the heating by the incident proton beam has been studied using the resonance scan technique, and the size of this effect has been determined for a neon gas target.