For example, consider the following Johnson counter,
Assuming that my initial state is 00, Should I start from the first flip flop or the second flip flop? How do i know and decide which flip flop to start from? The final states vary depending upon which flip flop I start.

 

hi,
In most counters it is required that a Reset circuit sets the initial counter state.
If not, just powering up, the counter state would be indeterminate.
E

 

Even after resetting it, there is the problem of (when writing the states table) of whether first it's flip flop 1 or flip flop 2. Both are interdependent on each other. If I start from flip flop1, write flip flop 2's state based upon that, it's different from starting from flip flop 2 and then 1.

 

hi DBS,
Look through this link.
https://en.wikipedia.org/wiki/Ring_counter

Also here on AAC
https://www.allaboutcircuits.com/textbook/digital/chpt-12/ring-counters/

E