It could be useful to (already) know many things, but another question is how to efficiently get to learn them, starting from what background. Once you are at graduate level, a lot more becomes accessible, so the first step is to get there.

My sequence meant to suggest a way of reaching that level by self-study, and getting a good grasp of basic tools of logic in the process. It's probably not the best way, but if you suggest improvements, they ought to be improvements in achieving this particular goal, not just things associated with elements of the original plan, such as "more math books". Other goal could be worthwhile too, but it would be better to state the different intention before proceeding.