No disrespect intended, but that is a pretty abysmal session plan...for anyone; there are far to many isolation movements involved and only three compound movements (bench, pull ups, squats).
As a beginner, you can make great gains with compound movements alone (exercises that use more than one muscle), so I would focus on: bench press, press, row, squat, and deadlift. Those five exercises will work everything, but if you feel that a certain part of your body isn't responding the way it should then you can add an isolation exercise here and there. (A lot depends on what you have access to in your gym though).
A couple of caveats:
Learn correct form! - The internet is full of great videos on how to perform movements correctly. Watch them. Learn. If you learn how to do it incorrectly you are setting yourself up for injury. Better yet, get someone to show you at the gym.
Get yourself cleared for exercise by a professional - It's all well and good taking someone's advice over the internet, but I don't know how bad your back is or by how much/little it affects your physical abilities. Would you even be able to do a deadlift or squat, for example, without messing yourself up?