If you want a hardwood, go with poplar. I you want a soft wood go with pine. Either will paint well, and at a reasonable cost.
Poplar is very common for painted projects. Most people don't like how the greenish tint of the wood finishes with stains.
MDF is fine for painted panels. If you are planning on raising the panels make sure you have good dust collection at you router table/shaper. The dust created from routed MDF is terrible, and terrible for your lungs.
The only time where I have heard MDF to sometimes be a questionable choice, is in a damp setting. It probably depends on how or how well it was finished, as to how it holds up.