WooCommerce turns a WordPress site into a shop: products, cart, checkout, taxes. You keep your content and your catalogue in one place. That is the point.
Fit
Good when the site is already WordPress and the catalogue is not an enterprise beast. Less good when you wanted Shopify’s hosted checkout and no server to tend.
Setup that lasts
Official payment plugins. Shipping you can explain. As few extra plugins as possible. Test checkout on a phone.
Cost
The core is free. Payments, premium extensions and hosting are not. Budget those before you promise a launch date.