Hey HDFC and ICICI Prudential are both good. Please don't go for Axis Max. I'll tell you the pros and cons of going through online or intermediaries.
Online : When you go online you would get a slightly better rate ~2 to 5% depending on the plan and company compared to intermediary but post sales support will be minimal
Bank agent : Better avoid this channel as they don't give a good rate and also forget about any sort of support
Insurance Advisor : Slightly better rate than banks as advisor can almost match the discount given online (Yes, there are options to give discounts by giving up some commission). Post sales support like Clark support is the best as you can call up the advisor and he/ she will have contact with the claims team internally.
And this is important because you don't want your loved ones to run from pillar to post for claiming the insurance during some of the toughest times in their lives. So the extra 2 to 5% is definitely worth it.
Disclosure: I'm a financial advisor and insurance advisor as well. You can contact me if you have any doubts
