Do not delete or change anything, download and try the gmail ios app, see if you like it.

If you like your existing mail app, you can keep it.

What you are going to do is to try different apps to see if you prefer a non-Apple mail app for reading, writing and replying to emails.

You keep the exisiting Apple mail app either way. Internal apps, like messaging and sharing are still going to use the internal Apple mail.app and it's settings for default account, so you leave those general mail account settings there, but you can turn off the check for new email if you prefer the gmail ios app or other non-Apple mail app as your mail reading app. You can even replace the mail.app icon with a different one if you want to do that, without deleting anything or deleting any settings for your gmail mail accounts in settings.

You can move the apple mail app to an empty app page at the end of your list if you decide to use the gmail app as your primary app. You can also turn off all it's notifications in notification center in case you decide to use a different mail app.

If all your email is gmail-based, you could also try the ios Mailbox app. It's pretty good. The downside is they cache your email on their own servers. Up to you if that's an issue or not. But Mailbox supports push and it's a nice app IMO. Same thing, you can replace the icon on your device, but don't delete the default mail app or delete any mail account settings from it. These other apps work in parallel and have their own settings for the accounts they use.

-David