Panama is in general a casual city, with formal attire being used on special occasions. Despite the heat you will find that most residents opt for light pants or jeans, though you may want to ignore this standard for comfort sake! At night you will find that people dress up a bit for dining out or to enjoy the local nightlife. Many bars have dress code standards, which can usually be summarized by no tennis shoes or hats. Inexpensive clothing is also abundant thanks to the next door international shipping route known as the Panama Canal, so anything you overlook can always be purchased in downtown or the Albrook shopping mall (adjacent to the domestic airport).
While the climate is predominantly warm and muggy, the highland areas can be cold, and a sweater is recommended. This would include trips to El Valle or Boquete. For the lowland areas (basically everywhere especially David and coastal areas) light, loose-fitting shirts and shorts, capris or skirts are essential. If you plan to hike in the national parks bring boots and a hat or cap, light long pants, sunscreen, binoculars, repellent, sunglasses, etc.
Remember to take into consideration any extra tours that you will be doing that might require specific attire like jeans (horseback riding), a long sleeve cover-up (fishing or long boat trips) and of course your bathing suit! And again, Panama is an extremely affordable destination, so almost anything that you forget at home can be purchased here at the same price or cheaper.