HatepaperDoll, the Wonder was the first Disney ship I went on and she is beautiful!
There will be a formal night, and probably an semi-formal night as well on a 9 nighter. You don't have to dress up though, although the majority of people do. However, I've seen everything in the dining rooms from shorts to full on ball gowns (and have always wondered how they had the space in their luggage to pack one!).
Despite being a Disney cruise, it isn't in your face Disney if that makes sense. For example, whilst the artwork on the ship is Disney themed, its all very classic and beautiful, not cartoon and cheap/kiddie looking if that makes sense!
There are plenty of characters around, the times will be in your daily navigator as to which characters and where they will be. Up to you whether you go and queue up and meet them or not.
Usually on cruises of 7 nights or longer there is a character breakfast. They have changed how this is done now in that if you want to go, you need to book it (its free, you just need to make that choice), so again, totally up to you whether you do it.
There are shows on every night. There are Disney ones (the new Tangled one is amazing!) and they are like Broadway shows. However, there are always a variety of other entertainers onboard as well, and again, you don't have to do the shows. There is a cinema which tends to have all the latest releases, if something is opening whilst you are on the ship you will also get to see it on there. On the TV in your cabin there are all kids of films on. There is also "funnel vision", which is a massive screen on one of the funnels by the family pools, and they tend to play the classics. Again, the Navigator tells you what is on. I remember one evening lying on a lounger under a blanket at bout 11pm watching Cool Runnings!
The kids clubs are great. My kids were older when I discovered Disney Cruises, so started in Edge, which I think is 11-13 or 14, then there is Vibe which is 13 or 14 to 17. My kids absolutely love the clubs, I literally never see them other than for dinner. When we cruised in May my DS was gutted he is now too old (18). He loves the clubs so much he is doing childcare at college and plans on applying to work in them when he is 21.
There are a couple of forums that are good - the disboards is an American one that has a huge section about Disney Cruises, also if you are so inclined there will be a meet up thread about your cruise which you can join and get chatting to other people, someone will usually start a fish extender group etc (fish extenders are basically so called because you hang something on the fish hook outside your cabin, and other people put gifts in for you, and you do it for them. Can be great fun but also a bit of a bind. I've joined in 5 times and loved it). There is also the dibb, which is a UK one about all things Disney and again has a section for cruises (not just Disney, all types). I think cruise critic has a forum section for Disney Cruises too.
Best thing to do is read your Navigator each day. It will be delivered the night before when your cabin is made up for the evening, and will tell you everything that is going on the next day.