OK, then one idea is to check for real estate auctions of farmland. Farms in the area often have a body of water that has been used for stock or irrigation. Some of these can be quite large. You can also look on
ValleyMLS.com which lists north Alabama and southern Tennessee properties.
When you talk about lake properties in the area, people generally think you want a lake that you can go boating on. The Tennessee River is more or less a chain of lakes that remains at a constant level, similar in appearance to the southern part of Lake Champlain, but in some areas you may find lakes have severe fluctuations due to power and flood control activities, or because of drought.
Many people think of Tennessee as a low tax haven, but you have to study the various counties and towns to get the mix of services vs. taxes that you want. Property in an unincorporated area of a rural county with minimal government will have low taxes, but a house within city limits will pay considerably more. Be aware that some places have fire association dues, or other expenses that can bring costs up.