[stefanos82]

About WooCommerce: Go for it, but be ready for some customizations to meet your own needs.

Use the plugins you need, else if you have the knowledge implement the whole mechanism yourself either in a series of small custom plugins or place the whole custom code inside your theme's `functions.php`.

My suggestion would be the following:

    * go with a VPS
    * choose NGINX for web server and reverse proxy
    * setup microcaching
    * use memcached or Redis if microcaching does not cover your needs
    * use the latest PHP
    * avoid using a plugin for image optimization; let NGINX do that for you
    * if there's a need for a REST communication, use WooCommerce's REST API; it works wonders!

That's all I can remember for now.

So, TLDR; yes, you can go with WooCommerce and communicate with your own CRM's APIs without a sweat.

How do I know?

Well, I have done that for a customer. It's a custom solution that updates their stock on a daily basis multiple times and every 15 minutes it automatically synchronizes the necessary changes; else, there's the "run now" option to immediate execute the synchronization upon demand.