Although one can only assume who Mary Shelley desired her target audience to be, her introduction to the 1831 publication to Frankenstein could provide some insight into who Shelley thought would read her novel.
The typical readers of horror stories are those who desire to feel the anxiety which arises when reading horror novels and stories. Based upon the stereotype, one could assume that Shelley's target audience was the horror seeker.
Outside of any stating by Shelley, in regards to her target audience, one's reading of the introduction (1831) to the novel could offer insight into the targeted reader.
I recurred to my ghost story, my tiresome unlucky ghost story! O! if I could only contrive one which would frighten my reader as I myself had been frightened that night! What terrified me will terrify others; and I need only describe the spectre which had haunted my midnight pillow.
Here, one could assume that Mary Shelley's targeted audience was the ones who desired to be frightened. Given her own nightmare triggered the ghost story, Shelley (most likely) believed that her target audience would be those who desired to read stories similar to the nightmares they had.
In the end, Shelley wished to simply "terrify others." Those others would be defined by those who decided to pick up the book. Curiously enough, in the same 1831 introduction, Mary Shelley gave credit to her husband (Percy Bysshe Shelley) for writing the novel.
As far as I can recollect, it was entirely written by him.