Personal thoughts on how to choose Vaccine as of date in India given tremendous uncertainty about approval/availability of Vaccines.

If you can get it "somehow" .Get a Pfizer/Moderna Vaccine . Previously it appeared that Pfizer Vaccine would come in Private Market and will be administered in Metros.

But Pfizer developed cold feet and Govt seems not interested (as Vaccine requires -70 degree for storage and distribution difficult/price high-> could precipitate health iniquity).

As a compromise ,if you are very high risk(>50,comorbidity, elderly in family). Consider taking Covishield. Hold off/get Antibody titres if you have autoimmune/neurological disease or history of severe allergic reaction as here the Vaccine has higher risk of side effects

While approval in Clinical trial mode is granted for COVAXIN . Wait for phase 3 data . (don't get sucked in by "indigenous" tag yet).