As a general rule, you are allowed to take three pieces of luggage free of charge (2 large items and 1 small briefcase/rucksack/laptop bag, etc.). Excess luggage and bulky items may be carried subject to available space and charge. However, unless the luggage you are carrying is excessive, they are generally not overly strict. An extra handbag or laptop bag should not be a problem.
Most trains have small overhead luggage racks for smaller bags and jackets, and at least 1 luggage compartment per carriage at the ends of the carriages.
Be aware that you will need to be able to get your own luggage onto and off the trains, and that everything must be clearly labelled (just as you would when flying). Although it is generally very safe, it is best to keep an eye on your belongings.
