Feel free to wear gloves when handling the wetsuit. The rubber that the wetsuit is made of is vulnerable to nails and sharp objects.
The wetsuit should be tight, especially around the sleeves / wrists, legs and around the neck (to prevent cold water from seeping in)
The wetsuit should have some water in it, this will be warmed up by body heat, thus keeping the body warm during the activity.
Feel free to try out the suit before you compete, so that you know that it fits and is comfortable. You should have good movement in the shoulders in particular, so that the wetsuit gives you good conditions for swimming.
You may want to apply a little Vaseline to the edge around the neck and the suit, to avoid chafing.