From this pdf (Reconsidering Sputnik: Forty Years Since the Soviet Satellite) at NASA.gov referring to Sergei Korolev, the lead rocket engineer for the Sputnik project:
There were many debates on the shape of the first satellite, with most senior OKB-1 designers preferring a conical form since it fit well with the nose cone of the rocket. At a meeting early in the year, Korolev had a change-of-heart and suggested a metal sphere at least one meter in diameter. There were six major guidelines followed in the construction of PS-l:
- the satellite would have to be of maximum simplicity and reliability while keeping in mind that methods used for the spacecraft
would be used in future projects;
- the body of the satellite was to be spherical in order to determine atmospheric density in its path;
- the satellite was to be equipped with radio equipment working on at least two wavelengths of sufficient power to be tracked by amateurs
and to obtain data on the propagation of radio waves through the
atmosphere;
- the antennae were to be designed so as to not affect the intensity of the radio signals due to spinning;
- the power sources were to be onboard batteries ensuring work for two to three weeks; and
- the attachment of the satellite to the core stage would be such that there would be no failure to separate.
Also (interestingly, in my opinion at least), according to the contents of that same pdf, apparently it was polished in an attempt to help prevent it from overheating:
"Korolev came over to the shop and insisted that both halves of the
sputnik's metallic sphere be polished until they shone, that they be
spotlessly clean," recalled Konstantin Feoktistov, who would be the
first engineer-cosmonaut to go into orbit in the three-man Voskhod 1
seven years later. "The people who developed the radio equipment were
actually the ones demanding this. They were afraid of the system
overheating, and they wanted the orbiting sphere to reflect as many
rays of the Sun as possible."