I usually bring cash and two bank cards, for withdrawing money from the machines. Be sure to inform your bank(s) you'll be in the DR, so your cards aren't flagged for fraud. If you bring a substantial amount of cash, try to stay somewhere that has a safe in the room you sleep.
Cash is always accepted. Credit/Debit cards are accepted in most larger businesses although you may find that you will have to pay a surcharge to cover the business's commission to the credit card company. On the other hand, many places will give a "discount" on the price if you pay cash - don't be too shy, be sure to ask.
Travelers' checks are very uncommon and a hassle to deal with even in the capital and tourist areas.
You don't mention where you will be staying or what you'll be doing whilst you're here, but the usual vacation "common-sense" guidelines apply. Keep your travel documents and valuables in a secure place, don't have lots of visible jewelry or expensive electronics including cellphone, don't flash cash around and don't carry more than you can afford to lose.
I favor debit cards over credit cards, a worry that was expressed above.
Cash, not too much, is fine. There are "Casas de Cambio" all around.
Check a few to see what the going rate is, and then choose one. Banco Santa Cruz, Vimenca (Western Union) are major players in the money exchange market, so they usually give you a fair deal. NEVER, EVER change money in the street.
As additional advice, photocopy your docs and leave the real ones in a save place, like a hotel safe or your room safe.