Hi Linda,
Personally I would take a mixture of cash and cards. If you don't have a credit card, you should be able to use your debit card to withdraw cash from ATMs, but check with your bank before you go and let them know when you are travelling.
Travellers cheques are OK but can be a pain to get changed.
Another option is to get a pre-paid cash card, which allows you to load on money in advance and use like you would a credit card. There are plenty of these around, a popular one is offered by the Post Office,
Kind regards,
Ben