This looks like the perfect project for the Magento platform.
I've been working with Magento since 2011. Since then, I've developed custom extensions, new themes, and managed day to day operations for mid-sized websites. Magento is a very powerful platform, but it does require some level of expertise, and attention to details. This is especially important if you need to scale up, as intended in this project!
I suggest using Magento 2.1 along with a branded theme. I recommend Porto, which is pretty powerful and allows for customization. Magento itself brings all of the basic features of a e-commerce website: customer, product & categories admin, several payment gateways, multiple shipping methods, CMS support for static website, support for promotions, among other things.
Other important things to consider: global taxes, global shipping, returns management (RMA), and a customer helpdesk.
My proposal has a budget of $15000 to build & deliver a beta version, with the main functionality. Some things (taxes, shipping), require external services with ongoing costs. My estimate of support & maintenance costs is between $1500-$3000/month, depending on these services and the ongoing work you want to do on an ongoing basis.
I'll be happy to answer any questions about the project. Freelancer.com doesn't allow bids that are too lengthy, but I'm available over the chat if you need more info.
Looking forward to it!
Leonardo