I am having trouble finalizing my choices for university.
For a little background, I am applying for math. I have A*A*A* predicted in math, further math and physics. I am also doing an EPQ artefact that consists of a learning resource on fairly complicated mathematical topic. This last thing related to epq is relevant since it might help differentiate me from other applicants. Also, I would say that my personal statement is quite strong as it highlights quite a lot of interest in the subject, and I feel as if the stuff I did quite stands out.
Now, my issue lies in which universities I should pick on UCAS. At the moment I am fairly confident I want to apply to Cambridge, Imperial, Warick and Durham. And for my last option I was thinking of either Edinburgh or Bath. Now I am unsure which one to pick. Edinburgh has a higher ranking than bath, but I liked bath much more when I visited. Also, bath has higher grade requirements with A*A*A (on the website it says A*AA but when I visited, they said that they changed the grade requirements but didn't update the website) and Edinburgh has A*AA -A*AB. This is important since all of the universities I'm applying to are not really safe options and I don't have any back up instead something happens.
My teacher told me to just pick what I like, and he said that what I'm aiming for are safe options for me. However, I am skeptical. I am worried of the scenario where I don't get any offers from my top picks: Cambridge, Imperial or Warick. I'm also worried that I might not meet the requirements for any university because all of my picks require A*A*A or more. Unless I pick Edinburgh as one of my options.
So, to summarize: Is Cambridge, Imperial, Warick, Durham and Bath a safe selection for myself? Is Edinburgh a much better option than Bath? Does the World ranking play a major role in the previous question?
Note I am an international student.