The top four changes you could make that will impact comfort are:
- Clipless pedals/shoes
Tires will change the ride more than anything else, including changing the actual frame of the bike. The stock tires on your bike are very durable but also very stiff and harsh riding. They feature thick casings and steel beads to hold the tire on the wheel. Nicer tires have more supple casings and lighter Kevlar beads (often referred to as "folding tires" because the tire can be folded flat, unlike ones with steel beads). High end tires such as Grand Bois, Schwalbe, Panaracer, Pacenti or Compass have very supple casings which turn results in a much smoother ride. Your bike can take just about any 700c tire. I'd strongly suggest something in the 30-38mm wide range. This will give you plenty of cushion but still be light enough that you won't feel like you're riding a tractor. Expect to spend $70-120 for a set of nice tires. The Panaracer Pasela Tour Guard in 35mm width is readily available and can be had for ~$40/each and is a nice mix of durability, lightweight, price and comfort.
Clipless pedals and shoes are going to be more comfortable and safer. Cycling shoes are like any other pair of shoes: what works for one person may not work for another. Try on several pairs. Like good running shoes, they should be snug but not tight. One tip (and this applies to all shoes): don't try them on in the morning. Your feet swell as the day goes by, always best to try shoes on at the end of the day. As for pedals there are numerous clipless pedal systems. Some people swear by one brand over others. I've ridden several brands and worked on pretty much all of them. They're all largely variations on the same theme, I wouldn't worry too much about one brand over another.
Saddles are also highly personal and costs can be as little as $20 or as high as $300+. I've worked with World Champion professional racers who are perfectly fine with riding cheap $20 saddles and I also know casual cyclists who absolutely swear by their expensive Brooks/Berthoud/Selle Italia/etc. Price really is no indicator of comfort. Replacing saddles is a pretty simple process and a good shop will take the time to let you test ride several different models. Do ask what their return policy is on saddles. A saddle which might feel fine on a short ride could become unbearable after a couple of hours.
Handlebars are a tougher one to fix. Most road bikes have drop handlebars which offer more hand positions and are more ergonomic. However, you really can't easily swap out handlebars as this requires new shifters and brake levers and that gets quite expensive. A simpler, less expensive solution are bar ends (example: http://www.rei.com/product/837362/profile-boxer-bar-ends-silver). These bolt to the end of the handlebar and help put your wrists in a more ergonomic position and provide you with an additional position to put your hands. You could also swap out the straight bars for a set with more hand positions and more swept back hand positions. You can see several examples at: http://www.somafab.com/parts/handlebar You will probably want to work with a shop on this as you may also need a different length stem.
Beyond this you start getting into things like replacing wheels which will cost a lot of money and result in very minimal returns. Ditto for brakes and shifters.