We always have two different Visa cards. One is a Capital One and the other a Chase.
The reason for this is that even if you each have a card they are still on the same account and if there is a problem both cards are canceled.
If you have two American Express cards then it is better in the event there is a problem with one of the cards. Each card has its own account number. The problem is that, like the commercial says, "They don't take American Express." Visa is far more widely accepted than Amex.
So: What we have with us are:
2 Visa Cards
$100 in smaller bills
Whatever interim cash we think we need.
If we need foreign currency we use our ATM card
I haven't used travelers checks in twenty years. They are basically worthless unless you are going to go to a bank or the customer service desk and cash them. Many retailers will not take travelers checks anymore.
I also can't understand why people will go to their bank and get thousands of dollars worth of Euros or other currency. Most banks charge a fee for this and why are they walking around with this much currency in their pockets. Just hit the ATM at the airport and get the amount of local currency you will need for smaller purchases and use your credit card for anything else.