Some additional points
When you check in, you will be asked for your credit card. The check in agent will take an imprint & issue you an on board credit card (may also be your room key) because there is a cashless system on board. You will use this card to purchase items on board (drinks, gifts, etc.). The only cash you need is to tip the room service waiter on delivery if you order room service & to tip your cabin steward, waiter, & bus boy at the end of the cruise. You do not need to carry your own personal credit card or cash until you leave the ship to go into a port. At the end of the cruise you will be given a statement listing the charges you made on board that will automatically be charged to your credit card. You could go down to the pursers desk & pay this bill in cash instead of having it go to your credit card, but is it worth it to stand on line when you could be having fun.
Millie has a coffee bar called the Cova Cafe. Desserts are free but coffee is not. If you want a cup of coffee in the casino or a lounge, you will likely be charged. The only places coffee, iced tea, & juice are free is in the dining room or the Ocean Grille/Cafe during regular dining hours. I am an iced tea drinker & this is the 1st ship I will be on that limits these "free" beverages.
If you go to the Celebrity Web Site, I believe under reservations, common questions there is a price list for beverages, i.e. wine by the glass, drinks, etc.
re: pampda comment on bringing your own wine on board. I thought this too but apparently Celebrity has changed their policy & are not allowing people to carry wine on board. However, all the boards I have read say they are not enforcing this. I plan to bring 2 bottles of wine, but I am prepared that they may take them from me upon boarding & return them to me when I disembark. It's a chance I'll take.
My DH & I will also be on the Millie in June. We sail the 21st. When do you sail?