There isn't much to do in Tengiz considering it's in the middle of nowhere. The closest town is Kulsari, which is an hour away. The main attraction in Tengiz is Shanyrak, a huge camp for the employees of TCO and PFD employees. There is a night club in the TCO camp called Aquarium which is not too bad. Other than that there's nothing to do.
Luggage and bags:
Bring TONS of warm clothes if you're travelling to Tengiz in winter. The temperatures go down to -50 with wind chill in January, February. It's extremely cold.
If you go there in the summer bring a barrel of mosquito repellent, there's millions if not billions of them there.
Clothing/Shoes/Weather Gear: Warm clothes
Toiletries and Medical Supplies: Mosquito repellent