Middle of March the weather should be good. You'd be amazed at how warm the desert sun can make you feel. Temps could be in the low sixties and if the skies are clear the sun's warmth will make it feel like the eighties!
If you are renting a car and you're limited on time, seeing the dam and taking the tour is a worth while trip for sure. Valley of Fire is a nice trip if you have a lot of time on your hands but for me that would not be a "must see."
"gamble, drink, gamble, drink, sleep, eat...and do it all over." You will not have any problems finding places to any of the above as well as shopping! Well maybe sleep may be a low priority.
Congrats on biting the bullet! I wish you all the best for sure.
If you happen to have Caesars Palace in your plans of places to visit during your trip, let me know, it would be cool to meet you!