Sorry Hunter, I got tied up at work and didn't reply very quickly.
There are two main ways to set up Gmail... and before I go on, this is gmail that you are talking about isn't it? I may be wrong but I only am aware of the Archive function with gmail. If it's not gmail you can disregard everything I say from now on.
If it is gmail, you can set it up in your email settings either by going to Mail -> Gmail, or Mail -> Exchange.
Basically the main differences are the Gmail way, pulls from the Gmail server every X amount of minutes that you set up. If you set up via Exchange, then the server pushes to the phone, which means you receive the emails as soon as the gmail server receives them, rather than getting a few emails at every interval when the app checks.
As far as I know, using the Gmail setup, you swipe and get the Archive option, but in the Exchange, you only get the Delete option, which gets rid of the email completely.
To try the Exchange model do the below, you can change back if you don't like it. I prefer it as you get emails immediately, just like you would an SMS.
1. Click on Settings > Mail, Contacts, Calendar > Add Account
2. Click on Microsoft Exchange (Very Top Button)
3. Enter your Gmail Address
4. Leave Domain Blank
5. Enter Username without the @gmail.com
6. Enter Password
7. Click on Next on the Keyboard until the Server box comes out.
8. In the Server Box, enter m.google.com
9. Click Save and in a couple of minutes, your Contacts from
Gmail should show up on your iPhone, and you should start receiving emails one at a time as they get sent to you.