You Trek looks like it would be a great bike for supported touring. I would concentrate right now on making sure it fits right -- that is, the correct saddle height and position, stem height and reach, handlebars adjusted (brake levers look awfully low to me). Find a good mechanic/bike shop that can evaluate your fit and offer suggestions.
Stay away from tubeless tires. You need some good quality clinchers, preferable folding because they are lighter, and at least 25 mm wide. You might want to consider fenders and a rear rack.
You seat comfort is also very important. Yours is an Avocet, which are supposed to be comfortable, but saddle comfort is very individual. See if your local bike shop will let you try some different models so you can find one that fits you. If all else fails, lots of cyclists have found that Brooks leather saddles are the most comfortable once you get the properly adjusted and broken in.