I have a very bad undergraduate percentage (BSc maths, 58.3%) and from a no-name university. Mostly because I was not interested in pure mathematics and gave all my time to CS components of the course. However, I worked hard and got admitted to one of the best research institute in India (CMI) for MSc CS and maintained a consistent A grade. I also bagged some good internships at very prestigious Indian institutes (IIT-K, ISI). I was also offered PhD position in CS at both CMI and ISI last year.
I wish to join PhD outside India mainly due to stipend (very low in India, wont be enough for a family of 3). However, my BSc marks keep haunting me and often leave me very disappointed.
What are my chances to make it to a good university (<300 rank) in US or European countries? How much does BSc marks matter for a PhD candidate?
Also, should I take a PhD position at a low rank institute (~700 rank) if the professor is well known and has very high research throughput?
Also what rank and how many colleges should I apply to to maximise my applied-accepted ratio?
Thank you very much for giving it time to read.