Using Suica and paper ticket together

I want to take a conventional limited express train and pay for the basic fare with my Suica card. When entering an automatic ticket gate, do I also have to insert the paper limited express ticket, or just tap my Suica and show my limited express ticket to the conductor on the train?

If you are using a Suica card as a payment method on a ticket machine, then you just need to use the paper ticket as normal though the gates, and do nothing with the Suica card.

You must first insert your limited express ticket and then tap your Suica (if you tap the Suica first, the machine will think you are only paying the base fare).

By the way, since limited express trains are long distance, do make sure you don't go beyond the Suica validity area.