Should I open a savings account in ICICI or HDFC?

Got a job they’re not opening a salary account but I have a shit bank currently which was a continuation of a student account from my college, I want to shift banks before onboarding. I need one that has the most consistent and rewarding offers across MMT, goibibo, book my show, swiggy zomato Myntra Amazon. Ig that’s either ICICI or HDFC. I’m new to all this so I’m just beginning to learn about RD and FD and all, should I be looking at interest rates? How do I know what I should go for? What else should I be looking at to choose? My money priorities rn are I want to save up for deposit and rent when I start house hunting in a couple of months, I live in Bangalore so the deposits are insane and I’m not looking for anything beyond 20k max for rent. And I want enough saved up so that worst case even if I get laid off I am able to survive for at least 3-4 months. Idk which type of savings is best for this goal. What investments do I go for and will that affect my choice of bank? Any help will be appreciated!