I read the contest rules. Lockheed/Martin sponsors a similar contest this is only a weightlifting event, but they specify an OS .65 AX as the power system with any prop they teams wants. Their electric category is one motor and battery combination too so that teams can focus on their airframe design instead of worrying about their power systems. To give you a useful answer, I can tell you that you'll want a low Kv motor running with a lot of voltage to turn a big shallow pitch prop. You'll need a lot of wing to meet the STOL requirement, and you'll probably do best in the taxi contest with a tail dragger with the tail wheel fairly high so that the nose isn't sitting up too much. Use the biggest wheels you can to handle those bumps, and consider buying the DuBro pneumatic tires since they are so much softer. If the data is available to you, look at previous designs that did well in similar contests to get an idea of what works and what doesn't.

I've worked the Lockheed contest a couple of times at my club field and have noticed a trend of students designing planes that are maxed out for straight line flight efficiency (some really elegant designs) but fail the practical test of turning well or being able to handle gusty wind. Watching novice pilots with their finely built but so horribly unforgiving airframe designs take them home in a plastic bag can be a hoot, especially when they walk around so cocky at the beginning. So my point is that the most technologically advanced design with the best airfoils for lift and the least draggy tails and such may not be a good move for you if you don't have an experienced pilot to fly the plane. Add unpredictable wind conditions to the mix, and going with a fairly easy flying plane has a lot going for it.