In a sense, we should see both. In reality, all the serum did was give Norman heightened strength, it didn't drive him mad. He was screwed up before, a neglectful parent, a cut-throat businessman and selfish to the point of insanity.
Becoming the Goblin isn't the act of someone who suddenly lost his mind, it's the act of a man who has - through his whole life - began to feel that social norms and values do not apply to him.
In the comics, Harry's drug addiction is a big trigger. So the mask, being an old Halloween toy, makes sense. He uses the mask because it's a symbol of his sons lost innocence and youth. In his sickened mind, what he's doing is defensible because he is merely standing up for his family.
That should be a big theme, the idea of 'family'. And how Norman's definition of it basically boils down to his own whims, all the while being adamant that he's a devoted family man who's doing it for his sons own good. He's truly deluded.
And we should see more of his delusions, before the serum, he should be suffering from hallucinations. The HulkGoblin thing could be a recurrent image he sees in his daily life. of course, we know that Spider-Man becomes a similar manifestation of his madness too.
But what if he was detached from the suit and literally believed that he was the Goblin creature? His speech would fluctuate between playful taunting and sibilant snarls and roaring.
By making the physical transformation another indication of his mental illness, we can have the best of both worlds.
It's especially captivating as Norman is a character who won't acknowledge the possibility that he's ill. I'd love to see his Social Darwinist streak early on.