If you have clear thoughts about your research area after your Bachelors then i you can go for integrated phd if not then go for msc and then write  NET JRF for the selection in phd program.

Because by the time you complete your Master's you can have clear idea about your research area and then i will be easy for you.

Also sticking to same institutes for  year is different than going for 2 different institutes as it will help you to gain more exposure.

All the best!!