BBA

You should pursue a course based on your interest areas & career aspiration. A 3 year LLB program will straight away give you a career option as a lawyer/legal advisory firm where as a BSC & BBA may not be able to get a good career break and you may be required to pursue an MBA program post-graduati

Yes, its worth every penny that you will spend.

Look, if you want to get into HR, then it does not really matter what was your graduation. BBA and LLB are both graduation level courses. So, leave them aside. So that leaves your MBA (HR) that too through correspondence. Preference always will be received by candidates who have done MBA full time.

Colleegs in Mumbai:
NMIMS-Mumbai
Colleges in Pune:
Symbiosis
Colleges in Hyderabad:
ICFAI Business School

It is very tough in any university, but you can visit ITM personally and have a check.

You can try commerce college Rajasthan and also have a look at top private universities such as Amity, Manipal or VGU-Jaipur.