I've used both Shopify and Wordpress with the WooCommerce plugin. Both setups work well. The choice depends on your needs.

Shopify is definitely a turnkey solution. It has built-in POS and inventory management and easily integrates with numerous selling channels as you've mentioned. There's a lite plan ($9/month) that doesn't give you an online store, but does allow you to sell products on Facebook and your own website. If you are looking to get up and running rather quickly, Shopify is the way to go.

Wordpress with WooCommerce takes a bit more effort to set up. While it's free, you'll need to host your site somewhere, so you'll need a web host that is optimized for WooCommerce. Also, to get the functionality that Shopify offers out-of-the-box, you'll want to add some plugins to WooCommerce. You may also want to upgrade to a paid theme to further customize your shop. So, using Wordpress with WooCommerce may not end up being less expensive than Shopify. The main advantage of using Wordpress with WooCommerce is that you have much greater flexibility in customizing your store.

If you are looking to quickly open up a standard online store, then Shopify is your best bet. If you are willing to put in some time and are looking for a more customized store, then go with Wordpress with WooCommerce.

We started with Shopify and then switched to Wordpress with WooCommerce as our needs grew and we wanted some custom features in our store that were difficult or impossible to do on Shopify.

Good luck!