Thank you, that's good to know. I will just take my stainless steel water bottle and refill it.
We have used them several times and gotten personal service from their agent Donald Percell. He has gotten us upgrades, and has replied to questions at all hours. That said, normally, we shop cruises through VTG, but actually book direct with the cruise line. Since you are going on your first, even though you are getting (ahem) excellent advice here, Donald might be your best bet.
The problem is that bottles of water can easily be emptied and filled with alcohol. Some cruise lines no longer allow bottles of water or soda to be brought on board, at embarkation or at port. Mainly because people dump the water out, fill with vodka (or other clear spirits). Cuts in to the cruise line profits. Going through security once for a three night cruise, I saw someone with a HUGE bottle of mouthwash that security was inspecting. Much more mouthwash than any one or two people would need for a three night cruise. While there is always the benefit of the doubt, I doubt it was mouthwash in that bottle.
No. Security may find it when scanning your bags and either allow you to take it on or confiscate it based on their policy. Most lines want you to carry on any water or soda rather than put it in your luggage you leave with the porter. If you put it in checked bags, then they may not deliver your bags and ask you to pick them up and tell you what they removed. Of course all based on their policy and thoroughness of x ray.
You will find bottled water in your cabin. Those original ones are free. You can refill them onboard. There is chilled, filtered water in the buffet room. If you use the bottles that will replace the original ones, you will be charged. I would NOT put water bottles in my luggage. Perhaps some booze, but not water
you will not be asked at the check-in counter. 
Did you take into account the $ amount of the Costco cash card that you get back after your cruise? I have compared VTG, Costco, Crucon etc and find that Costco and Crucon are better than VTG. I believe Crucon has change fees and I won't touch them. VTG also has change fees. Costco's site is easy to use and understand the final cost.
I remember on the first cruise I ever took I scoured the internet for information, trip reports, pictures, etc. of the particular cruise we were doing. Once I got onboard it was deja vu. I felt like I'd already done all the things we were doing! It did distract a bit from the whole experience. So save a little bit to discover once you're on the cruise. But, do your due diligence, of course, for the best deal you can find for yourself. Hope you have a great trip!
Celebrity and Royal Caribbean recently updated their policy to twelve 500ml bottles of water or non-alcoholic beverages per cabin as hand carry only.
It is posted on both the Celebrity and Royal Caribbean cruise critic forums, with link to their new policy. I will look for it tomorrow and post the links.