Fastmail....It is not free, but I find it to be fantastic. I use the email, contacts, and calendar, and it works perfectly with your iPhone. Specifically, Fastmail has "true" push as the emails sync among all of your devices. For example, if you read and delete an email on your iPhone, the delete status will update on your iPad. Also, the contacts and calendar are now "push" as well. Give it a try, they have a 30 day free trial. And no, I am in no way affiliated with Fastmail. I was just looking for a good, dependable service other than Google and iCloud, and during my research, I found many folks talking about Fastmail. The cost is $3/ month for there basic plan that comes with 2 GB of storage and $5/ month for their plan that comes with 25GB of storage. For me, this is very reasonable.