With any electrical testing there are two methods adopted.
1) Jumping to likely faults
2) Sequential testing
The former can be quicker but also can fail the latter will find the fault. Working in a factory where there are plans and all cables are accessible using the latter makes good sense but in a house with many cables buried one can only guess on routes and one has to jump to likely faults.
Some pointers though are:-
1) Check the bulbs are good.
2) Do not use energy saving bulbs to fault find with.
3) Invest in a cable finder and good meters.
4) Make notes.
5) Enquire about work undertaken in house.
As time goes on one finds repeated faults for example one whole sale outlet in my area was selling populated consumer units and they would place the MCB’s in the unit. In theory the electrician fitting the unit should check the tightness of all screws but in fact they would only tighten those they had used and it became a common fault to find the screw connecting the MCB to the bus bar was lose. So it for a time became first item to check. An old poor quality transistor radio is a good tool as it will crackle with sparks from bad connections especially if off channel. In industrial premises we often used a heat gun to find faults where items were hard to access. There is really no magic wand just a lot of thought on each system.
With domestic lights one would try to work out the likely route and check the lamp before the one not working.
So there is no real correct order as such.
You must also remember on forums like this you may get 100’s of people reading a post and acting on it even though it is aimed at you. It I suggested the first place to look is the consumer unit and explained how to remove the protective covers and test the output from the 6 amp MCB there would be a high chance others with little or no experience will also try that method and be unaware of the dangers from ionisation try measuring with the meter on the wrong range and suffer very nasty burns as a result. Because of this I don’t recommend methods which if I was answering the same post on the IET forum designed for the trade would be recommended without much hesitation. The other point is you have talked about India and although they may follow some of our practices I could very easy direct you completely wrong.
Having worked in Algeria, Falklands, and Hong Kong plus working on Dutch, German and Turkish systems I realise how easy it would be to give completely wrong information. For example the Dutch system I worked on had the switch after the bottle fuses so fuses always connected to a Phase and there were special tools to allow live working. Your general questions are good but will get very general answers.
All best Eric