The type of wood you use will vary depending on where you are located. The type of wood that is used for the dimensional lumber (i.e. 2x4s and 2x6s) that is used for framing houses in your neck of the woods should be just fine. We are based in North Carolina, where pine is plentiful and inexpensive, so that's what we use and recommend around here. The people at your local lumber yard or home improvement center will be able to advise you about what is used in your area.
It will likely be a softwood such as pine, fir, spruce, or cedar. You don't have to use a hardwood like oak, maple, or poplar, unless that's what you prefer. Hardwoods will be much more expensive than softwoods though.