I would like to send Recurring Billing & Subscription Management emails to my clients, which SMTP should I use.

I think that we need more information to tell you something relevant. For example the volume you think you will send, if you want use SFP-DKIM-DMARC on your own domain, etc.

Anyway, I can suggest you read this article. It could clarify some doubt:

http://www.emailvendorselection.com/choosing-between-a-cloud-and-on-premises-mta/

Lorenzo

If you are planning to send subscription invoices, recurring bills and other transaction details to your customer via emails, then there are many subscription management softwares that allow other software integrations like MailGet, Mailchimp, Aweber and more  

But if you want to do email advertisements and promotion of your products & services than, I would recommend that a dedicated email marketing tool will be enough.

Premium Email Marketing Services:-

• SendinBlue
• MailGet Bolt
• Get Response
• Aweber

These are some blogs that will help you find Subscription management solutions:-

• Cheapest Recurring Billing Software
• 10 Smarter Billing Tools For Subscription Businesses
• Best Subscription Management Software For Recurring Bills