The first spacecraft to achieve escape velocity (11.2 kilometers per second) and the first to reach the Moon was Lunik 1 (Lunik in Russian term is Luna in English term). Obviously the first target had to be the Moon since it is so close: Lunik 1 was the first successful attempt made by the Russians in 1959. Lunik 1 bypassed the Moon, Lunik 2 crash-landed there, and Lunik 3 went on a 'round trip' sending back the first pictures of the far side of the Moon which can never be seen from Earth because it is always turned away from me.
Source: my humble memory