I believe artists need an email service provider that offers marketing automation features. For that reason, I suggest Mailerlite.com. It is free for the first 1,000 subscribers and with low prices for larger lists. I find it easy to use. Its drag and drop templates make creating beautiful emails a snap.
I used to suggest MailChimp because it also has a generous free starter account. However, it doesn't have marketing automation to set up funnels and drip campaigns. You can do some of that in MailChimp, but it is hard to set up and not nearly as user-friendly as Mailerlite.
(August 2017 update) MailChimp according to some of my artist friend users has started allowing free users access to all its features. Further, they report it has made improvements to its automation and tagging features. I have not personally checked these changes out, but am happy to learn they are in place. As such, it may be worth considering now more than in the past.
Here is a description from Hubspot:
Marketing automation refers to the software that exists with the goal of automating marketing actions. Many marketing departments have to automate repetitive tasks such as emails, social media, and other website actions. The technology of marketing automation makes these tasks easier.
Examples of marketing automation for artists are sequences for welcome emails, thank you for your purchase, (including anniversary of purchase emails), nice to meet you at the show, thanks for your inquiry on my website, and many more. The point is to have a series of pre-written emails that are sent when triggered by some action or event.
Having sequences for different subscribers who are interested in certain kinds of your work. For instance, prints versus originals, or sculptures. Any time you can segment your audience and get them into a sequence, you are dialing in on their needs and wants and not just blasting everyone with the same message.