Which credit card to apply for? Axis Neo as first card?

So I have been working for 5 yrs but with 0 credit card and credit score.

Will be getting a house in the future so need a card for building good credit score. Salary account is axis and they are offering NEO as LFT.

But I was eying icic Amazon pay but it's showing invite only. Also asked for axis ace as LFT since I have axis account for almost 8yrs with decent savings balance but they are not giving as LFT

I pay all the bills for my family - rent, bills, fuel, groceries etc etc. Can I go with neo or any other LTF cc would be better?

Please suggest!!