Ash, Oak, Beech, Birch, Hickory and Hard Maple are by far the best types of wood to use. They each produce a high amount of heat, which is one of the most important considerations. Each of these species burn extremely well, and they are all relatively easy to split. Another feature of these types is that they produce very little heavy smoke and very few sparks.
Aside from the species mentioned above, Soft Maple, Black Cherry, and Yellow Pine are the next best to use. The Soft Maple and Black Cherry each produce a decent amount of heat, but they both burn well and are easy to split. They also produce a low amount of heavy smoke and sparks. Yellow Pine is also quite a decent wood to use. The only significant drawback with Pine is that it tends to smoke a lot, and it may not be ideal for burning inside your home.
Elm, Sweetgum, Basswood, Poplar, and White Pine are all decent species. If you are unable to get any of the wood mentioned above, these will work just fine. None of them produce an impressive amount of heat, but in certain cases some heat is better than none. These species also produce more smoke and sparks than the aforementioned. The Elm and Sweetgum tend not to burn very well, and they are often difficult to split. These woods should be used when you have no other choices available to you.
As is the case with any heating system, your wood-burning stove should be installed by a professional. It must be checked and maintained annually, along with your chimney. Remember to always make safety a priority, and to keep your fireplace tools and fire extinguisher close by in case of an emergency.