A typical amount of luggage is 2 large items per person, plus one smaller item or “carry-on”. You would not have to pass through customs or any x-ray machine.
There is no checked luggage for trains in Europe. Passengers carry their luggage on board the train with them. Sufficient luggage storage is provided in both 1st and 2nd Class. There will be room for luggage storage above and below each seat, as well as at the end of the train car in certain cases.