Blanket
He chose a blanket. He preferred a soft duvet, but a warm fleece throw is much more practical given the situation. His friends had told him many ideas on how to use this covering to his advantage in the Games— the obvious ones being for comfort when sleeping (but quick naps only, of course), and for protection from the harsh elements. He was taught how to use a blanket, in dire situations, and when folded in a certain way, to descend safely into caves. His teacher advised him that he should use the blanket to carry his belongings in, from campsite to campsite.
But at the front of his mind, he had always planned that the blanket was to be used in the time between his death and when the drones came to remove his body from the arena. However short or long that period of time may be, he wanted to make sure his body could be kept somewhat safe. He and his district partner had an agreement they would do this for each other.
He found it to be quite the gift that he got to choose what he would be wrapped in when they would return him back to his family in District 8, where textiles were produced.