You need to watch the first, second, and last serials of the First Doctor era, as the second serial introduces the Daleks, and the Cybermen, in their debut, were the last villains he fought before his first regeneration. The second Doctor, watch the War Games. I'd say to watch any episode involving a companion leaving or joining, but the second Doctor's longest serving companion, Jamie McCrimmon, debuted in The Gunfighters, which is now wiped. :(
I recommend looking up episode summaries on
http://tardis.wikia.com - you can get a list of episodes for each season by looking up Season ##.