I have never taken the hotel shuttle as the Bangkok taxis are generally easy and cheap, not uncomfortable, and will not slow you down on your exit from the airport as they are plentiful. However, for comfort alone taking the hotel car may be a nicer transition for you on your arrival to Bangkok. It should get you some water in the car, nicer car, a driver that will go a bit slower at a safe speed and the hotel will be ready for you.

If price is of any concern to you, I would absolutely use a taxi the next day on your return. The hotel will hail the taxi and it will cost less than 500 baht/$17.

I would recommend a sightseeing tour of the temples as well. On such a tight timeline, I would hire a guide through the hotel (arranged before hand)so that you can maximize what you can see and not get caught up in the logistics - definitely Grand Palace and Wat Arun and Wat Pho as time allows. I would not recommed the shopping malls, although they are popular, 24 hours in Thailand don't make them a must see as they are similar to high end malls everywhere. I would recommend returning to the hotel after the temples to get ready for a Thai dinner (fancy or otherwise, you must focus on food in Thailand!) and then a stroll around Silom at night. Although cheap trinket shopping, great street food and glimpses of the red light district may not be high on your list, if you are interested in experiencing a bit of tourist Bangkok it will allow you to take advantage of your late evening time and see the city at night and full of energy.