just returned from eastern caribbean on Paradise. yes, keep it simple!
daytime.....khaki shorts and blouse or nice t-shirts will be fine for ship and shore excursions. don't forget exercise clothes if you're interested in gym or aerobics classes.
evenings.....i wore light sweater / sweater set and slacks and little black dress for formal nights (although there were a number of formal gowns.)
also, there were laundromats (on every other floor) on the ship so you can wash mid-week. ($2 wash, $1.50 dry and $.75 for detergent...fortunately, i brought dryer sheets as they weren't available on the ship.)
they also have irons and ironing boards in the laundromat for your use.