Don't even think about taking sterling travellers cheques to America ! And I wouldn't rely on taking any sterling notes either.
Cards are best, as you can withdraw a little everyday, and not have to carry so much cash around with you. Dollar travellers cheques are OK. You used to be able to use them in shops just like dollar notes but I am not sure if that is still the case over there. American Express are best...you can get a replacement within a day or so if they are stolen. Keep a separate record of every cheque and where and when you cashed it.
If you are going to use cards, take a couple with you and keep them in different places.
But please.....no sterling cheques !