The original Cybermen had to be upgraded from somewhere, and seeing that they share a human-like structure, were they humans? Or were they another species? Also, did the original Cybermen interact with Daleks?
The "original" Cybermen began as the humanoid inhabitants of Earth's sister planet Mondas. In the final 1st Doctor story, The Tenth Planet, we learn that the inhabitants of Mondas became Cybermen by gradually replaced their body parts with mechanical ones. These Cybermen are referred to in the fandom as Mondasian Cybermen.
In the the 10th Doctor episode The Rise of the Cybermen, we are introduced to a different breed of Cybermen that was created in an alternate universe by John Lumic, the head of Cybus Industries. These Cybermen appear to be created by directly "upgrading" human beings from that universe. These Cybermen are referred to in the fandom as the Cybus Cybermen. They can be distinguished from the Mondosian Cybermen by the "C" logo on their chests ("C" for Cybus). Thanks to DoctorWho22 for reminding me to mention the "C" logo.
As for interaction between Cybermen and Daleks, I don't believe there are any example of this until the revived series. We see the Cybermen fighting the Daleks in the 10th Doctor episode Doomsday. Cybermen and Daleks join forces to imprison the Doctor in the 11th Doctor Episode The Pandorica Opens. We also see Cybermen and Daleks in the final 11th Doctor episode The Time of the Doctor. Thanks to John Sensebe for reminding me to add this paragraph.