Which tires are best for on and off road use? My tires are worn out so I want to change them. 

When I am trying to change them, I want them to be to the best fit for the conditions I cycle in. I cycle about 30 km a day on roads ranging from smooth pitched roads to very rough roads consisting of pits and stones in the most haphazard way. 

Please suggest a type of tire that would be best for me. There do not need to be considerations for snow, it does not snow where I cycle.
What you are looking for is a hybrid tire with not enough tread to be a nuisance and slow you down on the road, but enough tred so that when you go off road you are not losing traction on gravel and mud. 

For example Bontrager makes a hybrid tire that is nice:


Also, go with the hard wall tires whenever you can. they cost a little more, but they are more puncture resistant. So they will cause you less grief on the road.