If budget is no object, and to best serve the needs of your users, I highly encourage you to take a mobile first philosophy. It will allow you to find the absolute essential features that users will need, that can be augmented for desktop and tablet, based on the available screen real estate and adding value to the experience. If you take a desktop first approach, especially if you believe that you will need to put every single feature on the mobile e-commerce site, you will end up with a overwhelming mobile experience.
Hard to believe, but not all features of a desktop e-commerce site need to be available on mobile -- yes, all payment processing, data-collection and selection criteria for a product need to be there, but as you evaluate your content with a mobile-first mindset, you will find that some elements of an item inventory dataset do not need to be displayed in mobile, but can be displayed on desktop. How you think about images when planning mobile-first, and the variety of sizes needed across devices will help you keep a light and nimble desktop experience because you are being conscious of the bandwidth issues for your mobile users - and that will trickle down to your desktop experience. Rather than a highly dense experience, you can create something light and joyful to engage with.
Whether you use responsive design may depend on your user base, the penetration of latest-gen smart phones among your users and whether you are a local, regional, national or international site, and whether you need to also accommodate a variety of languages and different user expectations.
It would be great to see a solid e-commerce site that was fully responsive, and that users can scale down to the available screen real estate they have. I liked the Tom's Shoes mini shopping module that followed you around the site. It was basically a mobile shopping experience attached to a larger web site.
If you have to support feature phones, you will probably have to build a separate mobile site for them, since most of those phones are not html5/css3 enabled. Take a look at the users, their devices and the percentage of sales your client already does on mobile (or their competitors). This number will grow. You want these users to be as happy as your desktop users, and you don't want them to feel like navigating your site is a burden - or that they are on a miniaturized version of the desktop site.