"Tonewood" alert... There is a school of thought that says wood species doesn't matter when it comes to solid instruments. I tend to think it's correct. A pickup is not a microphone - it doesn't "hear" the strings vibrating, but senses that vibration in a magnetic field and converts it to electrical energy.
So the important qualities are rigidity, weight and appearance. Any half decent piece of timber will do the job. As you plan to paint it, appearance is also irrelevant, although how well it takes finish is a consideration ("oilier" woods are more difficult in this regard). Construction - how well everything fits together, etc, quality of pickup and fittings - matters far more than materials. You could even use mdf, as do Danelectro. Have fun.