For sightseeing, casual clothing and good walking shoes are desirable and appropriate, and most cities don't require formal clothes, even for evenings. If you're doing business in Peru, you'll need the same attire you would wear in U.S. and European cities: for men, suits and ties; for women, suits for day wear, and for evening, depending on the occasion—ask your host or hostess—a cocktail dress or just a nice suit with a dressy blouse.
Travel in rain-forest areas will require long-sleeve shirts, long pants, socks, sneakers, a hat, a light waterproof jacket, a bathing suit (if you want to swim), sunscreen, and insect repellent. You can never have too many large resealable plastic bags, which are ideal for protecting official documents from rain and damp and quarantining stinky socks.
If you're visiting the Andes, bring a jacket and sweater, or acquire one of the hand-knit sweaters or ponchos crowding the marketplaces. Evening temperatures in Cusco are rarely above 40F. For beach vacations, you'll need lightweight sportswear, a bathing suit, a sun hat, and lots of sunscreen. Peruvians are fairly conservative, so don't wear bathing suits or other revealing clothing away from the beach.
Other useful items include a travel flashlight and extra batteries, a pocketknife with a bottle opener (put it in your checked luggage), a medical kit, binoculars, and a calculator to help with currency conversions. A sarong or light cotton blanket can have many uses: beach towel, picnic blanket, and cushion for hard seats and, most important, always travel with tissues or a roll of toilet paper, as restrooms are not always stocked with these necessities.