I prefer to finish furniture with polyurethane rather than paint, but paint has its advantages.  On a large piece like this, the internal pieces, back, and side pieces can be made from finished plywood saving money.  The paint hides the differences in wood variety.

 

I still used Brazilian cherry for the top, chest divider, drawer faces, and legs/corner supports.  I used the Brazilian cherry so that I could cut smooth routered edges and corners on the top and drawer faces.  I used it on the legs/corner supports for the additional strength.  

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I used a primer on the wood and then a white semi-gloss spray as the finish.  I made a painting decision I regret.  I used a brush and roller for the primer and the first finish coat on the internals of the dresser.  I did this because I hoped I could avoid spray painting in the garage.  However, all it did was make it more difficult to get a smooth finish, and, after I sanded down the brushed paint, I still had to spray paint in the garage to get a smooth finish.  Spray painting from the start, both primer and finish, was the best answer.