You should take these 5 things:
1. A really powerful telescope with a great camera and tripod,
2. Food, in a toothpaste tube.
3. Walking and climbing gear for lunar exploration.
4. A good communications device
5. Oxygen Reserves.
You should not take these:
1. Your pet (Might die)
2. Household belongings (You're not going to live on the moon, right?)