Best order management system for WordPress?

I run a business where I provide services.

Is there a plugin for WordPress that simplifies the ordering process and client management process?

Ideally, I’d like to have something in place where I can link to a payment submission page (for my ‘Order Now’ button), and from there there’d be a backend panel that displays orders which are in-progress and already completed. This way, keeping track of orders that need to be fulfilled will be simple and hassle-free. I’d also like to get email notifications for new orders, etc.

Does anybody know if something like this exists or how I can implement such a system for my website?

Thanks in advance.