Both the Barbados and US dollars are legal tender and are widely accepted. Please note though that change is most likely to be given in Barbados dollars only.
Traveler cheques are a personal preference in my opinion. They offer protection against theft but have the inconvenience of having to be changed as not all places accept them as currency.
As to how much money you'll need... how long is a piece of string?
Excursions usally cost in the region of US$ 50 to US$ 70 with some of them having lunch and unlimited drinks included. Meals can be had cheap (Chefette, local vendors) or hughly expensive (The Cliff, Restaurant at South Seas). Many bars do happy hours reducing the cost of drinks if planned properly.
Prices in the supermarket are relatively high, expect to pay through the nose if you insist on having English brands.
Mark