Either bar will work, and I have toured on my mountain bike with its flat bar, but I prefer drop bars for road touring. Drop bars provide two main advantages over flat bars.
First, drop bars allow you to use a number of different hand positions over the course of a ride. The different positions allow you not only to move your hand and arms around when they get tired, but they also change your entire position on the bike so that you are recruiting your leg muscles in different ways.
Second, drop bars allow you to adopt a more aerodynamic position. Now I realize this sounds silly given that a loaded touring bike has the aerodynamics of a dump truck, but it is nice to be able to get out of the wind at least a little when you face a day of headwinds.
I haven't seen this written anywhere, but I believe drop bars are also more comfortable over long distances because they place your wrist in a more natural positon. If you put arms out in front of you, it is probably more comfortable to have your palms facing eachother rather than facing the ground.
If drop bars scare you because they are low and far away, then by all means raise them and bring them closer. You are not racing, so you do not need an extreme racing position. If you are worried about braking from the top of the bars, consider getting a second brake lever (such as this
http://www.store.yahoo.com/cyclocrossworld/spookbraklev.html) that works with the existing brake lever.
Welcome to touring
Sean