Erin,
Two things I'd like to add. First, any offer that rewards with gift cards can be the target of fraud, so put some safety measures in place. Make sure you have some sort of validation step for those receiving gift cards, whether it's a manual validation, a second email that requires a click through, or a wait step (if you are rewarding a purchase). I've seen people create multiple fake email accounts to receive extra gift cards, or order something to get a gift card and then return the product or cancel the service.
Second, you can automate the whole process with a webhook to a vendor like Giftango (InComm). You can create an account with InComm and set up a smart campaign that either calls a webhook that goes and fetches an electronic gift card that you can insert into an email, or calls a webhook that triggers InComm to fulfill a plastic card via snail mail.
Hope that helps.