For the train you need to get a physical ticket. For the metro you get a token which has a chip and you place it on the turn style to enter. The train ticket can be purchased by cash or Easy Card, also called Yoyo card. It is a prepaid card which you can use to purchase train tickets, pay at convenience stores and can directly use it instead of the chipped token on the metro. The deposit is NTD 100 and you can probably turn it in at Songshan Airport when you leave for a refund. I don't think you can use a foreign credit card anywhere to get it, you will need a small amount of cash.

The train station ticket machines accept credit cards from memory but I am not sure they will accept all (or any) foreign credit cards. The same for the storage lockers. I have not seen a locker that accepts credit cards, but they may exist. Regardless, be aware a good number of credit card payment terminals in Taiwan do not accept all foreign credit cards. It is more likely the luggage locker will accept yoyo cards than foreign credit cards. If you are not going to many places a small amount of cash may be the simplest way to go. Otherwise you can get a yoyo card from a convenience store in Keelung Station.

Anyone with further information, please chip in! No pun intended....