Credit cards are your best option
This is a personal choice. I never use credit cards overseas except maybe for buying plane tickets if ever necessary. But I choose cheap hotels and do not eat in swanky restaurants or drink in expensive nightclubs.
I keep credit cards for emergencies and for some cash use debit cards in ATMs. I have no problem with bringing some cash from home and sometimes, depending on the country, even travelers checks. But not the low value currency or TC's. (For the majority of cash or travelers checks nothing less than $100 denominations for me.) Staying in cheaper hotels I have no big problems paying cash. My debit cards, through my credit union, pays for some of my ATM withdrawal charges and have lower fees than credit cards.
I never use credit or debit cards for cheap purchases in stores. I do see some tourists overseas using credit cards for really cheap purchases overseas, probably just like they would back home. But they are NOT back home! My opinion, the more you expose your credit card numbers the greater chance of fraud and more transaction expenses. (I trust an ATM more than a Seven Eleven or sandwich shop overseas.) Every now and then I notice when tourists are using ATMs for cash - they only take out a small amount. The fee to use an ATM is the same for the equivalent of $50 or around $450 - so take out the maximum!
If you rely on a single credit or debit card what happens when that card is lost or stolen or damaged or an ATM eats it? I would never rely solely on one single source for spending money.