As far as coaching institutes are considered, there is no such thing as ‘ The best coaching in Hyderabad‘. They all work on law of numbers.
The probability of your selection in IAS doesn’t depend on the coaching institute you join. It is, however, proportional to the amount of hard and smart work you put into your preparation.
In this internet age, when everything is available online, why do you want to sit for hours together in an institute, when on the other hand you could have gained more by same amount of self-study. In the end, there is no replacement for self- study.
I would recommend you to use internet to compile all material for each subject and paper according to the syllabus.
Guidance for the books to be referred has been mentioned in my other answers.
You can look up for strategy followed by selected candidates and use it to make your own strategy.
Start studying the standard books and reading newspapers. If anything is not clear from books, use Google, Youtube etc.
Make notes for static parts of the various subjects. Read a newspaper daily and think over the issue. Follow the important issues. Initially make notes out of newspaper to gather knowledge. Later you can go for current affairs compilation by various coaching institutes.
For optional, I can say that you can join a coaching institute as it requires in depth study and all material may not be available online. But here also, there is no replacement of self study.
Coaching institutes, however, can be very helpful for test series. You can take up both Prelims and Mains test series. This will help you to plan out your study and monitor your progress.