Bicycle Tutor

I have a Trek 1.2 road bike with a 56 cm frame . I'm 5' 9" tall and I'm comfortable with the seat height and stand over but my arms are rather short for my torso and I feel it's too much of a reach to the handle bars. I'm considering an adjustable stem in order to bring the handle bars closer thereby shortening the reach. Raising the stem angle would put me in a more upright position but that's ok. Is an adjustable stem, or at least one with a higher angle, the way to go or are there other options to shorten the reach? If using an adjustable stem at a higher angle is the solution would I want a longer stem length or a shorter one?

An adjustable stem will give you the chance to play around with the position. But probably better just to get a shorter stem. The adjustable ones are heavy and don't give you as much change as you might expect. You can get standard stems in a variety of lengths and heights.
First thing is to try to figure out where your hands should be. Maybe try going to a shop and sit on a few bikes. If you find one that feels good, measure from the seatpost clamp to the bars to figure out what length you need. You've also got to decide if you just want your hands closer or also higher. Then get the right size stem.
Short term fixes - push your seat forward a little, see if flipping your current stem over will raise your hands enough to feel better.
If this is your first aggressive road bike in a while, you might just give it a little time to adjust. But proper bike fit is tricky and should be done carefully, especially if you have any knee, back, etc. issues. Ask around at rides if anyone knows a shop with a guy who is good at it. Most shop employees know next to nothing about proper fit.