Trains are generally a suitable mode of travel. You can buy train tickets in several ways, so check with your department if you have a preferred method before you buy.
Please note that you must be able to document the journey, regardless of the ticketing method you use.
If you don't normally take the train to work, you can get reimbursed for ticket costs between the city where you live and the destination.
If you normally take the train to work, you can claim the cost of the ticket between the city where your workplace is located and the destination. In practice, this can be difficult to maintain, for example when using a travel card, so there should be room for a practical and pragmatic solution, as long as it is explained on the travel reimbursement form.