Sending DACA renewal paperwork through mail?

What is the best shipping method for sending the DACA renewal paperwork?

Priority? Priority Express?

And does it require a special envelope or will any letter envelope do?

Do it Priority Express so it gets there faster.

You wouldn't need an envelope if you do the Priority Express, unless I'm missing something here. You just put the application papers inside the Priority Express envelope.

I sent my application 2 years ago with just priority usps mail

it really depends on where you live, but if you want it guaranteed to be there a certain day then express.... although if you don't make it by the cut-off time it'll just ship the very next day. unless you use other means of shipping.