I use Android, but most of the apps must be also on the apple store.
This is what I recommend:
Google Inbox: it comes with your emails and you can add reminders too
I mostly use Google Keep and Todoist and also the calendar for appointments.
Thank you Ra8;
I was on android; just acquired Iphone;
I used Astrid to do manager on my android; a very handy app.
I cannot find it on app store nor itune store.

In fact, I need to be able to snooze items, repeated it and change it tone sound.
Dears,

I ended up using Errands App as a tasks/reminder.
I couldn't find better free for now.