Would it be a good idea to have swipe gestures (such as swipe left to delete and swipe right to archive - mailbox app is a good example) responsible for your app's main tasks? A lot of not so techy people also use handheld tablets these days. Although I plan on adding an introduction to make sure users are introduced to swipes quite early, I am not sure if users will be able to remember them coming back to app after say 10 days.
There's a lot apps with swipe gestures, like Clear, Twitter, Tweetbot, Mailbox and other, but from practice, I could say, that these actions are not very obvious and user have some problems with them.
So the best 2 recommendations are:
Provide walkthroughs (tour) about gestures on first time app launch (see Readtime or Limelight) and provide help button on every screen.
Dublicate actions with buttons (see Facebook app)
I'd say for mailbox app left and right swipe gestures are more natural for previous-next mail navigation. Delete and archive rather secondary actions.
Swipe navigation also could be familiar to the users, because it is used in others apps in a such way.
The easiest way to be more confident of your choice it to explore some competitors' apps.
With the exception of swipe as a scrolling action, swiping is one of the most non-discoverable user interfaces ever created. As a user, you have no way to know what swipe gestures are going to do unless you just start trying random swipes (or someone else tells you what they do). To make things worse, sometimes swiping with different numbers of fingers does different things. It's a usability nightmare.
Having any form of swipe perform a destructive action (such as delete) is a terrible idea. The first time a user encounters it, they will have no idea what they've done and most likely no idea how to undo the action.
An alternative could be to use a context menu when the user touches & holds (like Open in New Tab for links in Safari). But a lot of users don't know about that either.
Overall, I think it's better if essential functionality is available through visible screen elements.