Walkways are quite wide so a double buggy wouldn't be a problem. They are used to guests using various kinds of prams and mobility scooters depending on their needs so pretty much everywhere on the ship is accessible. The lifts get really busy on embarking and leaving the ship - be prepared to queue.
The Windjammer buffet restaurant is very popular and can get incredibly busy. Breakfast and lunch can be eaten in the main dining room - the choice isn't as wide as the buffet but it's less crowded and you are virtually guaranteed a table straightaway.
Download the app. A few days before departure it will update with the menus for your sailing and suggested (not at all compulsory) dress codes for theme nights. Personally I like the formal night(s) but there is a real mixture of outfits - some in tux/long dresses and some more casual. We liked looking at the menu to decide what we wanted to eat but also to see if we wanted to eat at a different restaurant if there was nothing that took our fancy in the main dining room.
You may want to take some dollars for tips. We tip the waiters in the dining room (you have assigned seating in the evening) and the same pair of waiters look after you for the entire voyage. We also leave a tip for the room steward. You don't have to tip separately as your cruise fare has gratuities added anyway.
If you aren't having a drinks package there are plenty of free drinks around the ship. Tea, coffee and fruit juices are available at breakfast (extra charge for freshly squeezed juice and premium coffees). Water dispensers are everywhere although you will be charged for bottled. Iced tea and still lemonade are free at lunch and dinner.
I've never used the kids club but they looked fantastic when we looked around them.
There's a website called "What's in Port" that gives loads of info about cruise ports that can be invaluable if you aren't doing any organised tours. For example you can see how far the cruise terminal is from the town and there's information about buses/taxis and "must see" places.