Hi Edmond,
We evaluated a number of email delivery providers just over a year ago and found that many of them offer tips on how to avoid ending up in the Spam folder. http://documentation.mailgun.com/best_practices.html and http://go.sendgrid.com/rs/sendgrid/images/SendGrid_Deliverability_Guide.pdf being great places to start.
MailChimp has a lot of extra features such as list management and templates. Because you're managing your own user lists and have a trigger for sending individual emails you may be better off using a service that just sends emails. Mailchimp have a subsidiary called Mandrill that does just that (http://mandrill.com/), but other big players include Mailgun (http://www.mailgun.com) and SendGrid (http://sendgrid.com/).
We ended up using Mailgun and have grown with them from sending 2 million emails a month to 10 million emails a month, and while every situation is different I can highly recommend them.
Hope that helps!

