I'm quite sure this recently acquired beauty is a Dieffenbachia, but I can't seem to figure out what kind. Also, I really can't find any list of all kinds with photos or other good identification details included, online. Is there some web-resource on plant/Dieffenbachia identification that I am missing?
This is not a Dieffenbachia but an Aglaonema. Likely this is the very common cultivar "Silver Queen" described here as "a hybrid selected from a cross between A. commutatum Schott ‘Treubii’ and A. nitidu". It could also be a cultivar called "Silver Bay". It has been grown under low light and not cut back for many years. This why you have the long stems.
These plants are reasonably trouble free and bud easily from old stalks. To make this plant look a little bushier I would cut it back hard. Cut off all the stems at four to six inches from the soil. Take the cuttings and trim back the stalks while retaining the leaves. Ensure each cutting has four to six inches of stem and root them in water. Provide more light for the plant and cuttings.
The stems in the pot should bud out within a month and the cuttings in water should root in about the same time. When the cuttings have a good root system you can start a new plant or put them back in the old one.
Likely this plant could do with a repotting. Remove the root ball from pot and cut two to three inches off the bottom of the plant. Add fresh soil less plant mix to the bottom of the pot and put the plant and root ball back in the same pot.
You will have a pretty funny looking plant for a while but it will look much better with more leaves.
Thanks to @kevinsky, I was able to find the species, which was actually an Aglaonema instead of a Dieffenbachia.
It is an Aglaonema B.J. Freeman, aka Cecilia.