Oak (season dried) is the best all around firewood.
Any dry hardwood will work well, but for keeping your chimney clean stay away from pine or other pine type trees that have a heavy pitch/sap content.
Oak is a favorite because it is a very dense hot burning firewood, that cuts and splits easily.
Birch also burns well, but because it is a less dense wood will burn faster (a good fire starter). Where efficiency is concerned any hard wood that is dry and you can get it cheap or free, that's what you might want to go for.
Elm and Box Elder are good, but they are hard to cut and split. They burn fine once you get it dry though.
Local saw mills will sell their trimmings (slab wood) quite cheap and it only needs to be cut to length.
So you have to factor in what your expenses are (truck, trailer, chain saw, splitter), cost of the wood, delivery, the system your using to burn it and of course your time and availability.
Catalytic wood burning stoves will deliver a longer more efficient burn, while cutting back on fuel consumption. (More heat output for less money)
What is the worst type of wood to burn?...
Unseasoned wood and wood that has high sap content are not advisable to burn in any sort of fireplace or wood stove. As for the "types", it is kind of a hard thing to nail down, since all types of wood have representatives that are good and representatives that are bad. Cottonwood is not very good stove wood. I have hear, that burning cottonwood has draw backs like, having to clean the chimney cap about once a month to prevent it from becoming obstructed by soot and creosote.