All Disney ships are beautiful and very well-maintained. Galveston as a port has its issues because it can be rocky sailing out of the Gulf of Mexico, and fog can sometimes delay embarkation and/or debarkation, and it is a bit cooler in winter than coastal Florida. The biggest issue imo is that Galveston cruises rarely go to
Castaway Cay these days, and that's
DCL's private island which you don't want to miss. If you can find a 7 nighter from Galveston that does go to Castaway Cay, nab it.
The Wonder and Magic are the ships that have or will have itineraries sailing from Galveston, and they are called the "classic" or "Magic class" ships. The Dream and Fantasy are the "Dream class" ships. The Magic and Wonder are mirror images in terms of their staterooms, so if you read stateroom reviews, whatever goes for the Magic will be true for the Wonder and vice versa (the portholes in Navigator Verandah staterooms have a different shape, but that's the only real difference). The same is true for the Dream and Fantasy.
The Dream class ships have some bells and whistles that the classic ships don't have, such as the AquaDuck water coaster (but your kids are probably too young for that, and the classics do have waterslides your kids can use), the Midship Detective Agency virtual scavenger hunt (the classics offer a paper-based scavenger hunt), miniature golf (it's a small course, anyway), an upcharge ice cream/sweets shop (there is still soft serve available 24/7 on the classics for free), and there are virtual portholes in inside staterooms on the Dream class, etc. So there are some extras on the Dream class that you could appreciate after sailing the classics, but it's nothing that makes or breaks a cruise.
There are advantages to the classic ships, too. The adult pool is better on the classics, and there are more hot tubs on the classics. On the Dream class, the family pool deck has no hot tubs, but on the classics, there are two hot tubs on the family pool deck, so you can relax in the hot tub while your kids play in the kids' pool. The staterooms are a bit bigger on the classics. Animator's Palate has a better design on the classics. There are fewer guests on the classics, so Castaway Cay is a bit less crowded when you sail there via a classic ship (although crowding is never really a problem). Both the classic and Dream class ships have the same quality of Disney entertainment. Imo the two best theater shows playing on DCL are Beauty and the Beast on the Dream, and Tangled on the Magic.
The Wish is DCL's brand new ship and it's getting raked over the coals by experienced DCL cruisers, fyi. I recommend getting acquainted with DCL via one of its four original ships. Sailing out of Galveston is a good place to start- no flights is a nice perk.