Manual vs. Automatic payments
Any payment gateway that is supported by WooCommerce will work with Subscriptio's subscriptions, but if it has no specific integration implemented for Subscriptio, then payments will be only manual, i.e. user will have to log in and do the payment for each renewal order.
To make sure user won't forget about that, there's email notifications about new order is available, as well as payment reminder emails - all having convenient "pay now" button.
You'll need to use built-in gateways to enable automatic payments. Note that those also support 'normal' orders without subscriptions, so you can use our gateways as main for your site. In this case "pay now" button in emails is also available, though that's just an option - user doesn't need to make payment manually, even though it is still possible.