I found that when I ran curly maple through the planer it tended to tear out, at least with my machine. I started this project with a piece of 1.5" thick curly maple. I had originally planned a thinner base but I took the path of least resistance and made the base very thick. The wood was very flat and just need a bit of touching up.
To make the vertical slats I cut thin wood using the bandsaw from the 1.5" thick piece. To make these pieces flat and uniformly thick I used my hand planes. I found that the task of making the wood uniformly thick was not as difficult as I feared, at least on small pieces like this. However, I did find that I had to take shavings smaller than 0.002 inches thick or the wood would tear out.