Belle is also my favorite princess! Like everyone said, the Disney Dream is a great option for you. While not quite as immersive as Be Our Guest, Royal Court restaurant gives off the same vibe. Definitely understand where you’re coming from regarding the show but do make sure you see it during your voyage (it is only performed on the Disney Dream and Disney Treasure). It’s the best interpretation of Beauty and the Beast I’ve seen. Aesthetically it draws more from the 2017 live action but it’s way better than that film. 

The Dream sails 3 and 4 nights out of Ft Lauderdale. For your first time sailing, I’d recommend a 4 night. The 3 just feels too rushed. 

There’s a really helpful page on DCL website about paying for your cruise and what’s included: https://disneycruise.disney.go.com/paying-for-a-disney-cruise/?

If you’re booking far enough out, and not booking a “guaranteed rate” where DCL picks the room for you, you only need to put down a 20% deposit on the voyage and then you can continue to make interest free payments at the frequency of your choice until final payment is due. You do need to make these payments manually yourself but there’s a helpful calculator tool once you’re looking at prices that can help you see what the weekly, monthly, etc costs would be to pay it off.