You can get high deliverability -- the keys, whether you're using your own servers or someone else's come down to a clean list that won't generate complaints and staying within the TOS of your mailserver host or third-party SMTP service.

Host your mail-creation/list-management/analytics stack yourself (I like Mautic and MailWizz but there are other options) and use a third party for SMTP services. Amazon SES charges $1 per 10,000 emails; other services are slightly more expensive but it's all still very affordable.