What shelves to get for a china cabinet?
Since you're painting anyway, it doesn't make much sense to use the more expensive hardwoods like quarter-sawn white oak or blistered maple - quite ordinary poplar should do very nicely unless you plan to put a huge amount of weight on those shelves. Poplar is strong and dense, and it paints exceptionally well.

Note that you'll need to edge-laminate two or more planks to get your full 15" depth if you use poplar.

Another entirely viable option would be to use 3/4" MDF. It comes in sheets (you can often buy half-sheets and quarter-sheets). It's very heavy (about 96 pounds per full sheet). It's also very rigid and dense and takes paint very well. So well, in fact, that it's sometimes used as an inexpensive siding on condos. It doesn't tolerate moisture, though, so be sure to fully paint all surfaces.