Wooden Cart rehab project

I picked up this wooden cart at an estate sale for 10 bucks.  I'm not really sure if it is old or if it is just dirty!  Either way, what I needed it for, it will be outside in the brutal south Florida sun so it is probably better if it isn't some valuable antique.

The above picture is after about half an hour of sanding with an electric sander.  I didn't get a close up shot, but there were wooden pieces that were flailing out at the bottom so I pulled on them and sure enough, whole chunks of some sort of wood paneling came peeling off.  My 3-year-old got a kick out of helping me pull these off.  But after peeling them & sanding the flimsy board underneath, I'm realizing that I'm gonna need to do some sort of additional treatment to these sides.  The top and corner pieces are solid wood, so they are sound, I just will need a 'filler' for the center panel.  Especially since this side is the one that will be closest to the pool and likely splashed AND in the sun for half the day. 

I really liked these cool rusty wheels.  My husband suggested that I replace them, but I think they bring character so I'm leaving them. 

As I was sanding, I saw our dartboard case and thought that wainscoting would be a good idea for the flimsy side panel.  And, as you can see below... this is where it will be positioned so it makes sense.

I'd originally thought I'd stain it and treat it for being outdoors, but after seeing the inside of that side panel, I'm thinking paint.  I am not sure if I wanna do a slate gray that would look good with the stones on the house and that crazy orange door, or if I should go with a flat black to coordinate with the dartboard.  What do you think?