I have thought about after reading your question.
Mentally pack Confidence, Modesty, and humble pie.
Be confident in your ability
Be modest when you come off the line with a good score.
And when things don't go as planned be humble and DON'T give up. There WILL be times when you think you shouldn't be holding a rifle, it happens it is only one relay and you need to focus on the next relay.
Clothes, pack for two seasons a typical May long weekend (shirts shorts running shoes) and early spring, (Boots, gloves, warm jacket, toque) RAIN GEAR, and something to cover your rifle when it rains.
flip flops for the shower area
A LOCK for your room if staying in the barracks (combination lock) is preferred if sharing a room
When i stay at the barracks i bring a camping air mattress for extra cushioning on the barrack beds.
Good luck
Trevor