Yeap, I agree you should take $TC, You can use them as cash at most places (except food carts, Popcorn stands etc). but with £TC you would have to cash them in as nowhere will accept them as payment.
If your using them in the States, they need to be in dollars.
We take about $50 cash for use in the first day or so and the balance in travellers cheques. You'll need a few bills for tipping before you reach your destination (bag handlers, car rental, etc) and maybe for the toll road, if used.