I'm not a mother (but I am an aunt to 6 kids) so I guess take my ideas with a grain of salt. I'd go with some sort of adult lighting which complements the space (perhaps one hanging fixture, or a row of them on the beam?) And, add in some table lamps to make it cozy. I would think the main goal would be to make it nice and cozy for a small child. My view is that the decor should be functional and should not have to be changed out as the child grows. You can bring in the "fun" stuff with linens and other accessories, rather than getting a bunch of stuff a fickle child might not even like down the line (or appreciate at age 2 1/2) and which you'll just end up getting rid of. Then again, I have never really understood decorating children's rooms or nurseries in strongly "child-like" or baby colors and themes. ;-)

The style of the fan should coordinate with the style of your home, and you likely do not need a light in the fan. A lighting showroom can help you figure out the correct length of the downrod and the diameter of the blades. Just take your measurements in and they will assist you in getting the correct configuration.

My parents have a ceiling similar to that, and their recessed lighting ends up not shining on the main living area because it is so angled from the angle of the ceiling. Nevertheless, it's not a prohibitive thing to do recessed lighting. You just need to be prepared for where that light will end up hitting. A fan plus a chandelier could be a tough design problem to solve. Usually one or the other is the focal point. If you can find a nice light/chandelier combo that you like, perhaps that would work in the center of the room. There are people who specialize in lighting design. You might consider paying for an in-home consultation to see what other options you might have.

I love greens so it is a first pick for me. I am not a pro at any of this but love figuring out colors. To my eye the silver grey in the kitchen is fighting the granite a bit. The cabinets look good but they are more of a neutral color. I can see you have a wheat color in the hall, so more warm colors. I used BM edgewood grey in my house - prior to the remodel we are working on - and it worked well with my 1950 orangey red oak floors but was not overly warm/yellow for my taste. Read grey in some rooms/light and beige in others. Lots of grey and cool colors on these boards but honestly it doesn’t work in every house. Your dining room is really pretty and could be stunning with a bold color. Maybe let that lead and find a soft white or greige for the adjoining rooms. Good luck!