Attaching hard drive to Panoramic WiFi Gateway.

I think what OP is looking for is a better router equipped with a USB port.

OP was looking for "best" options. I consider a NAS a better option then a USB attached thumb drive. Not only can you get more performance and storage room, but you have more networking options. Also, OP wanted something to work with the Panoramic gateway.

Oh, I meant a USB port to connect an external hard drive...not a thumb drive.

OP could purchase a complete external drive and connect to the USB port of the router or if OP has a spare or unused HDD (SATA), a hard-drive enclosure would be best.

I'm not promoting or endorsing (not that I'd matter), but Sabrent and Mediasonic have great features for enclosures.

That means buying a new router, USB enclosure for the HDD, and a HDD. The WD NAS comes with a 4TB HDD for 269$. I would say that's cheaper then upgrading to a new router(along with everything else you would need to buy) and still supports wireless TV boxes. Even if not, it's still a alternative to USB and worthy of mention IMO.

My option would only be good if OP has a spare HDD (2.5 or 3.5).  I wouldn't recommend purchasing an HDD.

My approach is just an external hard-drive shared from the router.

Yes, new router, if Pano doesn't support an active USB port.  An external HDD enclosure is less than $30.  Spare HDD would cost nothing.