Responsive web design for e-commerce website? [closed]

I'm going to build a big e-commerce website and client want that website should be for all user Desktop, Tablets and Smartphones. and budget is not a problem. Site is an e-commerce website lost of categories and products , "add to cart, checkout functions, credit card and paypal payment etc.

Would it be good to make responsive website with mobile first approach or it will be good to make separate website for mobile?

And if I go with separate website approach I cannot leave any feature of desktop website to make it on mobile because it's e-commerce website so every product, purchase system , form validation should be on mobile website too.

What would be good for users?