Chip readers are becoming more common in the U.S., so that should not be a problem for you at most larger stores & hotels. ATMs, gas stations, many smaller retailers, and mobile payment systems still mostly require swiping a magnetic card.
You are often given the option to select "Credit or Debit" after swiping the card. Which one works can be inconsistent. Try "Credit" first and see, and if it fails try "Debit" and enter your PIN.
Businesses that don't take cards will usually have a sign saying so. Most will also post a "Visa" or "Mastercard" (Maestro) sign on the door or near the checkout indicating that they accept those cards (either debit or credit).
If your card has a "Visa" or "Mastercard" logo on it, and your bank is aware you're traveling internationally, you should be fine using it to make whatever purchases you need in the U.S.
Your bank/card might require inputting a PIN for each transaction. That's typical of debit cards in the U.S., but not credit cards. Obviously, ensure you have/know the PIN before traveling.
Do be aware of the exchange rate though, as well as any "international transaction" or currency conversion fees your bank charges, as those would be in addition to the U.S. dollar cost of your purchases.
Background for the "deferred debit" question:
In the U.S. a "debit card" transaction removes the funds directly from your bank (checking) account, usually within 24hrs if not immediately. Same as writing a paper check, or withdrawing cash from that account to buy something - it requires that you have adequate funds in the account at the time of purchase.
A U.S. "credit card" accumulates all the charges during a 1-month billing cycle, at which point you pay off all or part of the balance from some other account. These cards/accounts do not require you to have funds at the time of purchase - you just need to pay the card off eventually, usually at a substantial interest rate.
You can use either kind of card to make most payments in the U.S.
Again, if you have any type of "Visa" card, you should be fine.
The German system is kind of a mix of the above - all charges accumulate over the course of the month like a credit card, but then you automatically pay off the balance when the bank deducts funds from the same connected account, like a debit card. So "deferred debit" is a pretty accurate description. (In the U.S. this is similar to a "charge card," of which "American Express" is about the only example around - it's not as popular or as accepted).
The key issue is that if you don't have adequate funds in the account to cover all the charges, you could be in trouble. Whether the card/bank would decline charges that exceed your available account balance, or if they'd charge you overdraft fees/interest is up to your specific bank.
