Since no one else has chimed in yet I thought I'd start.
Firstly, I'm not a Professional cinematographer, I'm a storyboard artist for animation. Many of the principles apply just the same, though, especially when it comes to composition.
Before anything else, I might suggest that whatever thesis you decide on, that it's a good rule of thumb to narrow it down pretty tightly so you don't end up spreading yourself too thin over too broad a subject. Obviously, entire books are written on the general subject of composition.
Also I'd recommend another book that I love by Bruce Block.
His general ideas focus on 'contrast and affinity' as it relates to visual storytelling and symbolism.
I'll give you some of the challenges I face in my storyboards as well as what little I've done in live action.
Is my composition clear? Does it have good silhouette value? In other words, would the scene 'read' to a viewer if it were reduced to black and white? This concept is common in animation as it relates to character's body-language and performance, but you see it in movies, paintings, etc.(The Mysterious Geographic Explorations of Jasper Morello, 2005)
Am I conveying what the story needs to get across at this point? Revealing information to a viewer that they need at that moment, and if so, how? In a clever and entertaining way visually?
Is the composition reinforcing a story point? Like if a character is feeling lost, alone, insignificant, do you put the camera low and up at them to make the appear huge in the frame? Or do you put the camera high up looking down on them so they are small in the frame, perhaps with strong, angled, sharp shapes to create visual danger?
How do we want the audience to relate to a shot?
Do we want them uncomfortably close to a subject. Abstractly far away? Eye level? Maybe it's a P.O.V. of a child and so we're seeing compositions from a lower level.
Is a character experiencing calm moments at points, signified by more balanced shapes with the camera locked down, only to be contrasted by unbalanced hand-held shots when things are more chaotic? Maybe work is boring and repetitive, so the composition is flat with left/right motion. But then home life is boisterous and the camera is in motion as characters in in and out of deep space.
Are the compositions becoming more intense as a scene gets more intense? Like angles getting progressively stronger when Orson Welles kills the man in the motel room in Touch of Evil.
So another challenge might be whether or not something is even physically possible where you're shooting. Let's say you're on a low budget movie and you have a lot more limitations on what you can do. Maybe the location you have can't accommodate something you had in mind so you rework a way to get across the emotion, or whatever, with the elements you have at hand.
Before I sign off I'll mention in the challenge that's inherent in aspect ratio.
These days it's mostly 16x9 on tv and 1.85 or 2.35 for film, but for decades most movies were in the 1.33 'canvas' so when things got wider, I'm sure it was like reworking the mindset. Some filmmakers didn't really like the wider canvas. Fritz Lang said of CinemaScope: “It's only good for funerals and snakes.” ... Others found ways of creating compositions withing the canvas, framing things through doorways etc.
Years ago we started boarding in 16x9 panels assuming the TV's would be going that direction, but we still had to compose withing a 4x3 within the panel since most people at the time would be viewing the shows on tube TV's. Lot of empty space on the edges of those boards.
When I first start thumb nailing a script, my biggest hurdle is where to put the camera so that basic screen direction can be maintained throughout the sequence.
OK that's all I've got today.
Best of luck!