You can use woocoommerce subscription plugin and do billing using wordpress itself, if you prefer to do so. But you cannot automate or link the server directly with wordpress without using WHMCS or other hosting billing and management system.

Also there are some problems with wordpress as billing system, you cannot provide your customer an account portal to check his due date, invoices, susbcripton status and much more.. So lot of limitations, Also you need to find out how you are goung to offer invoices to your customers, will you use zoho invoice or something?

I suggest to get WHMCS, you can link it with wordpress using wordpress whmcs bridge plugin. Else you can create sub domain for hosting whmcs and setup customer portal on it. Either way, WHMCS will make things easy for you and help you focus on marketing, customer support instead of doing most things manually. Hope this helps you.