You will find parents, strollers, and crowds everywhere. The prices, in terms of expense, are the same at all the theme parks in the area. I know you say you prefer IOA/US and SW, but they keep their prices on par with Disney, for both admission and merchandise, so that's really not a factor.
Also, everyone is required to wear shirts and shoes in the park, no exceptions unless the child is an infant, and cannot walk. Anyone walking will be required to wear shoes. It doesn't matter how much you protest, it's a safety thing, and Disney is all about safety.
In terms of why MK is best, well, it offers the most attractions in one park, and the greatest variety. What to focus on? Well, there's so much! You didn't offer more than ages for your kids, so I'll be general ... Head straight to Fantasyland and get Fastpasses for the whole family for Peter Pan. It's not to be missed for any age. From there, it's up to you. The whole family will enjoy (Adventureland) Jungle Cruise and Pirates, (Liberty Square) Haunted Mansion, (Fantasyland) Peter Pan, Mickey's Philharmagic, and Winnie the Pooh, (Tomorrowland) Buzz Lightyear's Space Ranger Spin, and the Peoplemover.
There are other, significant attractions, that some in your family may enjoy, and some may not. Adventureland has Aladdin's Magic Carpets (a dumbo style spinner), and the Tiki room. Frontierland has Country Bears (for the younger two), and Splash and Thunder Mountain (40" height limit for both - Splash is a flume ride, you may get soaked, and has a 50' drop. Also, it may be in refurb, as it often in through January and part of February. Thunder is a roller coaster, no large drops, lots of fun). Fantasyland has Small World (a must for the younger ones), Dumbo, the Carousel, and Snow White (can be scary). Tomorrowland has the Speedway (the whole family might like this, but the younger set alway does, height to ride alone is 54"), Stitch's Great Escape (dark, confined spaces, 40" height limit, the Astro Orbiter (another spinner, good for the younger set), and Space Mountain (44" height limit, wild-mouse style coaster in the dark).
Currently, Main Street Electrical is the parade running at night, and you would also be able to experience Wishes, which is typically run every night.
WDW is in a slow season for part of February, and generally things start to get busy again right before President's Day weekend. Prior to that, waits will be short ... The parks will likely be chilly (to us Floridians), if not downright cold. It's a pretty decent time to visit, actually.