The first story that I have a recollection of viewing is the first part of the e-space trilogy 'Full Circle'. I remember the spiders in the melons very clearly.
But this is not the first story that I could remember in its entirity. This is Peter Davidsons 'Earthshock'. Having started to write this I now realise I remember Adrics first and last episodes vividly when growing up, his last in more detail

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I digress, Earthshock I found a very interesting story, firstly there was the caves being explored on earth, this is where we meet the doctor, the survey team and the androids guarding the hatch.

The Hatch concealed a bomb that would blow up Earth, to prevent this the Doctor traces the android controlling signal to a freighter. When the doctor lands on the freighter we are now fully aware that he is facing a fearsome foe, the Cybermen are back! The story then has the introduction of Beryl Reid as the ships captain, class. The whole ship contains thousands of Cybermen. The gold badge that adric had for mathematical excellence is used to kill some Cybermen and plenty of gunfights occur. At the end the Cybermen have locked the freighter on a collision course with Earth which Adric tries to prevent by solving the code, however during this the freighter skips 65 million years back in time. Adric cant unlock the final code as a Cyberman shoots the lock and the freighter crashes into earth causing the big bang. The end I think is the only story not to have the dr who them over the credits. Instead we see Adrics mathematical badge in silence.
I often wonder how this ending and the klling of Skaroth the Last of the Jagoroth fit together as surely that makes two big bangs?! Any way this is my first fully remembered story from my childhood.