The ‘brown’ of the wooden palette and the ‘brown’ of the imprimatura [brown underpainting] go hand in hand in oil painting. Mixing on a wooden palette gives you a good idea how the color will look on the canvas.
As for cleaning a wooden palette, you’ve got to do it after each painting session. I’ve found that if I let the mixed paint in the middle dry, then have to scrape it, I’ll eventually put gouges in the wood and work like the devil to clean it. Also, the palette has to be oiled down after each session. It should also be oiled on both sides before using.
If you palette of colors changes depending on the type of painting you do, you might want to have multiple palettes. You can just keep adding paint to the globs of colors on the rim of the wooden palette. This ‘saves’ the paint rather than wasting it by lifting it off the palette. But, the middle has to be clean to avoid mixing mud. So, if your palette of colors are split primaries, for instance, you’d want a different palette for you traditional 12 or so color palette.
Get the largest palette you can handle if you decide to hold it. If you lay it on a table, then get the largest you can find. It’s got more mixing room.