The first part of your New Customer Welcome campaign should include an email that has a few goals.
This email would go to new customers right after their first order. It's different than the welcome emails used when someone subscribes to your mailing list.
Long enough. Before anything else, make sure the email is long enough. You aren't writing a tweet, nor a novel. I'm seeing a lot of companies cutting their content to the bone and that's going to make retention more difficult. Make sure you have actual text content and not just images. You want your customers to be able to find this email again by searching later.
Offer help. The most important part of this email is to welcome the new customer and offer help. Tell them how to reach you if they need to: by replying to the email, phone, or if you have a physical storefront. Invite them to contact you and reply like a person. Most likely they'll be waiting to get your products and have a positive attitude. You might get a few upset ones, which gives you the opportunity to try to solve their issues early on.
Soft-recommend complimentary products. You want to gently introduce other products. Keep this small, no more than 1/5th of the email content. If you know other products that complement what they ordered, include them in the email. Especially if they are from different product categories. If you're email provider doesn't know what specifically the customer ordered, you can list your popular products as long as they have a wide range of categories.
Send this email to every new customer to kick start the relationship. Use it to start building rapport and customer loyalty. Your later emails can build on this and gradually shift to more product and sales-focused messages.
For advice on how to plan and when to send those later emails, use the 1-to-2 Customers focus page and Latency metrics in Repeat Customer Insights. Those metrics will give you an idea how long your New Customer Welcome campaign needs to be and how many emails to get started with.
Track down which customer cohorts perform the best
Different groups of people behave differently. Repeat Customer Insights creates cohort groups for you automatically to see how your customers change over time and spot new behavior trends.