I use what ever wood suits me at the moment. Or more importantly whatever is available for cheap!
I'm not familiar with Paulownia so I can't say.
Pine can be difficult because it has bands of hard and soft wood that make up the rings of the tree. The soft and hard rings can make the surface of the lure appear wavy because the soft wood sands away easier that the hard rings.
Poplar is an excellent choice, considered a hardwood but is very soft and easy to shape. I use a lot of it because a lot of interior trim is made from poplar and I get scraps from work.
I have a bunch of walnut from a tree I had cut up so I've made some of those. A little hard to carve but has an awesome sound to it when you put a rattle in it because of its hardness. I use a scroll saw and dremel to shape it. Also less buoyant so works well for deep running, or suspended lures.
I came across some Cuban mahogany that is very buoyant and wonderful to carve, tight grained so it sands very smooth. Honduran mahogany would be similar but is a little more porus.
I've also used the PVC trim board and I like it but you do have to be cautious not to heat it when running power tools over it. Not a show stopper, just something to be aware of.
Purple heart is the hardest thing I've ever carved. Very dense and has oils in it that will burn the wood very easily with power tools. I actually made one where the spots on the lure were simply burnt in with a polishing head on my dremel. Makes a great novelty "naked" lure when no paint is applied.
Maple, very hard but looks good on a naked lure.
Cherry is pretty hard but easier that maple and walnut to carve.
Bottom line is there is no right wood or best choice. What you have available is usually the best choice. But then, I don't make production lures. I do this to spend less money, have fun and to be creative.
My wife says I'm a procraftinator. But that is another thread.
Keith