3:16 p.m. on July 7, 2010 (EDT)
Welcome RickMan,
I have been fishing on backpacking trips for many years carrying basically what you describe in terms of gear. Most people carry way to much fishing stuff that they will likely not need.
As far as which flies to take, that is not up to you or me, that is up to the fish!
You will have to find out what the fish are eating in the area you will be backpacking in, and that varies widely from one month to the next, with some flies like terrestrials being good all year in certain locations.
You can cut a fish open and look in it's stomach to see what they are feeding on, I personally don't find that method all that great. First of all you have to kill a fish which you may or may not eat, it may be a strictly C&R body of water, you may or may not observe any stomach contents, and lastly this forces you to carry a large assortment of flies with you since you will not know for sure what the fish are eating until you get to the stream. The method is useful for refining your fly choices, but if you caught the fish on a fly, just keep using that same fly, why change?
Another way is to just look around to see which insects are present in the air, on plants & trees, or living in the water. Some insects spend most of their life in the water only emerging long enough to reproduce and die. This method also has the disadvantage of forcing you to carry a large assortment of flies, then choosing which ones to try once you are at the stream, river, or lake.
A better, easier method would be to find one or several online fly fishing forums that have online charts for different areas that tell you what the fish are likely eating at any given time of the year. From this chart you decide on which flies to bring, including any similar variants.
I could tell you all about how I fish where I go backpacking and it may have very little or no relevance to your area.
My advise would to be to talk to people familiar with the area you are going to, and most certainly find an online fly fishing forum with current info for your area.
Here is one to get you started, I have linked to their hatch chart page:
http://www.coloradofishing.net/hatch.htm
Hope that helps.