No, Carnival isn't bottom of the barrel. Too often Carnival gets a bad rap from people that haven't even sailed on Carnival. Also, too often people judge Carnival based on one cruise, and that one cruise may not have been a good fit for them. For example; short 3/4 day cruises are cheaper by nature and will naturally draw a variety of clientele looking for a cheap get-a-way. This may mean the affordability of a short cruise may draw a much younger, drinking, partying crowd. This is true on any cruise line offering the 3/4 day itineraries, not just Carnival. The person who may have wanted a quieter, relaxed cruise may not fit well on a 3/4 day cruise. They then turn around and bad mouth the cruise line based on that one cruise. When in fact it may have been a totally pleasant experience on a longer 7day cruise which draws a different crowd. Carnival carries more Senior citizens than any cruise line.
The three cruise lines sailing out of NYC each have a different experience. The three ships you named are all great ships. But again; they are each different experiences. First, your cruise should never be based on price alone. I would recommend you find a cruise oriented Travel Agent and let them help you on which one of these ships will meet the needs of your whole group. All three ships will have activities for the young and old. But a mega ship may be too much walking for the older people, unless they are very agile, then it might be just fine. These are some of the things to consider when planning for the whole group. The NCL ship offers Freestyle cruising which means you have total flexibility for dining times. However; if your whole group wants to dine together every night, it may be easier on Carnival or RCI with the assigned dining. Again, I recommend you find a cruise oriented Travel Agent to help you with this group.