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?)