This is why it's so important to book directly with an agent as they can be invaluable in helping you with all the questions and problems with booking a cruise, especially when doing your first cruise.
First, the Monarch of the Seas is a relatively smaller and older ship, and as such has fewer amenities. Plus, because of the age and size, it can sometimes offer a bit more movement than the newer larger ships that have better stabilizers.
Normally, I do not suggest any first-time cruiser select a cabin in the front of the ship. While at the time of year you're cruising, you should not encounter any rough seas, obviously there's not guarantee as Mother Nature can be very unpredictable. If there are any big waves, cabins in the front of the ship will definitely feel more motion than anywhere else on the ship. Which is why I usually advise first-time cruisers to look at cabins in the middle of the ship or at the very least in the back. The middle provides the smoothest ride, but will cost a bit more. Those in the back will cost about the same as those in the front, but sometimes you'll feel vibration of the engines.
If you handle motion well, you might do okay in the front, but keep in mind the motion on a ship is a different type of motion than what you get on small boats.
Nassau is one of those ports that people either love or hate - not too many people come out in the middle of that relationship.
As for safety, you'll be fine. Contrary to some of the reports you may read (the press always like to blow one or two instances out of proportion), cruising is very safe. Yes, you do have to take the normal precautions you would in any place where there are alot of people, but when you figure over 6 million Americans cruise every year, the amount of crime or problems is very minor compared to what you'll find in the average city.