I am confused how my dataset should look it. Should it contain only faces? Or, whole body? and, how should it be structured? And, how should the dataset look like?

My impression is that the first thing you have to do is recognizing faces before recognizing they are your faces. I don't know if those two levels of complexity are embedded in just one NN or if that make it more complex. I suggest to apply a convolutional to recognize human faces first and then a typical PCA to recognize they are yours.

I think for both cases you might need controls: situations where no faces are included, and then photos of other people different to you, otherwise the classifier will try to fit the image into an existing class.

That I think would be my first approach.

It will be always better if you provide more variety to the background (noise).