What BigCommerce already does for reviews
BigCommerce has product reviews built in, with a moderation queue. Store reviews only — nothing from outside.
If that covers what you need, use it. This is for the case where your reviews are spread across platforms your site cannot see.
The one thing to know about BigCommerce
Stencil themes need the script in the right region, and the region names differ between themes. Script Manager is the safer route because it survives a theme change.
Where reviews belong in a BigCommerce site
Through Script Manager for site-wide placement, or a widget region on a specific template.
Full-width sections suit carousel and grid layouts; sidebars and narrow columns suit a badge. Floating badges can be restricted to particular pages and to desktop or mobile.
Star ratings in Google search results
BigCommerce is the case where review markup does what people hope. The widget outputs Product schema with an AggregateRating, and Product is the type Google still shows star ratings for — the full explanation is here.
A product page carrying a star rating and a review count in the search result gets clicked more than the same page without one.