My advice would be to join the Grade 3 Government job as it will give you an opportunity to study for higher exams. It will also ensure many facilities that come with a government job like job security.
If you join HCL, with a 6 LPA package, the immense work pressure will hinder you from preparing for any further exams. You will have to keep climbing the corporate ladder and the pressure won’t let you prepare for your higher studies.