Chris, your suit will be just fine and a regular tie will work. Tux's only are worn by a small percentage of the passengers on most ships anymore. In fact, my husband got rid of his as he said a suit is much more comfortable when he is 'on vacation'.
Just remember that a cruise is what YOU want it to be. It can get very hectic if you want, or it can be the most relaxing vacation you have ever had. It's YOUR call and you do exactly what makes you happy, nothing rigid and take each moment as it comes.
Sometimes the ones that plan every second of their cruise out ahead of time are the ones that may get a little disappointed in the experience. There is so much to do, or not to do, but it is all your decision.
Hope you enjoy your first cruising experience!!!!