Very good question! And yes, having a picture or a story in mind is absolutely essential to a good performance.
The poetry part is your's to figure out. Use these pieces as an exercise to see if you can come up with a compelling story yourself. You'll need this skill throughout the rest of your piano playing career.
I guess I come from a different school of thought. I don't think it's necessary to have a picture or story in your head to create a successful performance. I
do think it is absolutely necessary to have concept in your head of the sound you want to produce in a particular composition. I think the danger of using pictures and stories when coming up with an interpretation is that you might force the music into a mould that is very different from what the score indicates and what the composer intended.
I'm not saying that you shouldn't let music create pictures in your mind, but I see it more as a
response to a successful performance than as the
impulse of successful performance.
If you focus on creating a good sound image in your head based on score study, and then work to create your sound ideal as you work, a good interpretation will result. This means careful score study of
all markings by the composer
form
key and chord structure
phrase and cadences
articulation
rhythm
polyphony and inner voices
points of emphasis, as well as places of tension and relaxation
dynamics
tempo, especially comparative tempi between sections
composer's life and motivation for composition of piece
comparative study with other works by the composer
study of historical period performance practice
comparative study of work in regards to similar works by composers of the same period.
And probably other ways of study that I forgot to mention.
Do all this and you'll come up with a well-founded and professional interpretation of the piece.
I guarantee you won't play it better if you just think something like...."Now here is where little Red Riding Hood is walking through the peaceful forest. The wave-like figurations of the right hand describe breezes gently stirring the boughs of the trees....etc. etc, barf, barf...."
Ok, I admit that was kind of a ridiculous story for the andante spinato, and probably not very valid. But, seriously, read some of the Hans van Bulow descriptions of the Chopin Preludes sometimes--they can sometimes be as silly.
So....what does Andante Spinato mean anyway....?