I use my default mail app, definitely. Sometimes it has sync issues - sometimes I know an email has come to me (ie, the sender tells me they just sent it; or I'm on my email account on my laptop and see that it has arrived) but it won't sync on my phone for a few minutes to an hour. Or sometimes the sync is automatic and I get the emails as I should. It's a little finicky but it's okay! I get my work emails just fine mostly.
As far as the calendar app, I use the "Event Flow Widget" app to better organise and display my upcoming appointments, events, etc. Doesn't do anything to my battery life and I really like the widget's transparency.