Mailchimp - Mailchimp is a great way to get started in building your email list. they also offer autoresponders as part of their offering.
Active Campaign - Active campaign is a site made specifically for ...well...campaigns. They also offer autoresponders as part of their campaign packages. To find out more about their autoresponders - check here: https://help.activecampaign.com/hc/en-us/articles/206535504-Autoresponder-campaigns