I too am a recent new owner of a Morgan. Mine is a Plus Four and it has a luggage rack fitted.
I think your idea of a nice suitcase on the back would complement your car but, when it rains, you will end up with a less than stylish soggy suit case.
I have a pal who is a "Land Rover across the desert guy" and I was chatting to him about luggage. He has loaned me a thing called a Peli case. It is black and water proof as well as bomb proof.
I looked these up on google and eBay and they are a bit expensive. However, if it meant that all your clothes stayed dry, on tour, then maybe they are worth it.
I also have a BMW bike and it has BMW panniers; they make the Peli case look really good value!
Just a thought for you.
Hope you enjoy your Morgan.
Axle Tramp