Yellow-poplar and oak are pretty popular hardwood species for log cabins. Granted, I've seen some log cabins made from other hardwood species: hickory, ash, sweetgum, basswood, etc. Some people tend to use what ever is native to their area. Each species tends to have its advantages and disadvantages as a log cabin wood.
Conifers are also commonly used: spruce, white pine, southern yellow pine, lodgepole pine, western redcedar, northern white-cedar, fir, Douglas-fir, baldcypress, and hemlock.
As far as obtaining these logs, please speak with your local state forestry agency or your state's extension forestry specialist.