Yes, it is the total cost you paid for the inventory. Remember, if you include the shipping cost in inventory, you will not separately deduct it as an ordinary business expense. Also, you will need to allocate the shipping cost to inventory as it is sold throughout the year to accurately account for the remaining inventory at the end of next year.
That wouldn't be proper. The cost of inventory includes the cost of shipping to you. Thus it should be allocated to the purchased items and deducted as the items are sold.