Personally, we opt to do nothing on our first night, and it's never seen us wrong so far. Too many things can go against you lol I don't think we've ever made it to our hotel on time; it's usually later!
Depending on what time you get up for your flight, you could be doing up to an 18-hour before you even make it to the hotel on the other side, and then have to adjust to the time difference. Although every person is difference, traveling is enough to tire anyone out.
You are going in September, right? Just bare in mind the hurricanes are active and can directly or indirectly affect your outbound flight. In 2007, our flight was delayed going out because it was coming from Jamaica and all flights there had been grounded due to the hurricane passing over. That night, we didn't make it to Pop until midnight, and by the time we get checked in and to our room, the food court was closed, and we had to order in Dominios Pizza - not so great for me since I can't eat pizza!
If the flight goes to plan and you arrive on time, then you have to get through Immigration. The lines don't move particularly fast, and if other flights have just landed you could be in for a long wait. Alternatively, you could be one of the few first off the plane, first in the queue and straight through with almost no wait - it's hard to say.
We were put on a ME bus in 2007 when our flight was delayed, and while it went to our hotel, it wasn't going to just our hotel. It went to Pop and all the All Star resorts. Fine for us as Pop was the first stop, but no so good if your hotel is the last stop. I don't know if there's a system you could find out as to which hotels are stopped at first, or whether it depends entirely on who is on the bus and going where.
There are quite a lot of variables that you have no control over, so while you could arrive at the hotel with several hours to spare before midnight, you might also find yourself arriving just on midnight. So, it's entirely up to you, but personally, I would not opt for a booked table meal on that first night.