How to customize store homepage?

So I’m attempting to create a WooCommerce store (puzzlesupply.net) but I can’t figure out how to really customize the home page.

Ideally I’d like to have a slide show followed by a list of 4 product categories followed by a popular products feed and maybe some other widget.

I’m currently using the Innovation theme but the only places where widgets are allowed is the sidebar and footer. I want to add widgets to the homepage itself.

Is this possible with a free theme?

What should I do?

Thanks!