Check the weather forecast for where you're going AND the entire upstream distance. A storm you cannot see or hear 75 or 100 miles away can spike the water level and catch you off-guard. Awakening at three in the morning to water lapping on your tent is NOT a pleasant experience. If possible, check the immediate weather pattern for the two or three days prior to your arrival. This can provide a good reference point for estimating water level.
When searching for a place to make camp, look for the debris line. This is naturally deposited material against stationary objects like trees or boulders. Or, it may just form a line on the bank where it settled when the water receded. Look to see if it's a fresh or older deposit. This will give you a good indication of recent water levels. This information along with the forecast will help you mitigate the risk to an acceptable level.
Although private property surrounds most of the distance, almost all rivers are held in the public trust and you have a right to navigate and enjoy them. (There is no legal distinction between rivers, streams and creeks.) There have been many challenges in the courts regarding property rights as they relate to waterways. In addition, there have been challenges to exactly what constitutes navigability. The SCOTUS has nonetheless made several rulings in favor of recreational usage. According to these rulings, the Kiamichi easily qualifies as a publicly accessible and navigable river as do virtually almost all other waterways in America.
Riverbanks are considered part of the river proper and you should camp there. A river's width has been legally recognized (but not formally defined) as the distance between the high waterlines on either side. However, it's impossible to be certain where they are unless the river is constantly in flood stage. A riverbank is commonly defined as the space between the water and vegetation lines. In some places higher (or normal) water levels might not even provide an accessible bank. Sometimes a river bank is completely vertical! Midstream gravel banks are fair game and NOT part of private property in almost all cases. Gravel bank camping is preferable to the forest floor, it's much cleaner and comfortable (depending on its coarseness). Popping embers won't start a forest fire and you don't have to deal with thorny vines or as many creepy-crawlies.
Albeit extremely remote, there is a always a chance you will encounter a hostile landowner. If you do it's a good idea to immediately declare your respect for their private property rights. State your intention to stay between the banks and leave nothing but footprints. Most of the time they simply want to know you're aware that. NEVER argue with a landowner who insists the river is part of their private property. It's better to move along and resume the issue with the local authorities at a later time. If this happens you should follow up on whatever corrective action they took. These are your undeniable civil rights. Besides, subsequent boaters could also be effected and you owe it to them. Just remember to be non-confrontational and respectful at all times. This is only an executive summary. If you want to read (much) more, please see the links below.
In sharp contrast with the city it gets dark much faster in the backcountry, especially under the forest canopy. As a rule of thumb, you should begin looking for a campsite at least 2 hours before sunset. Sometimes it may take a while to find a suitable spot.
When you get home, make a point to look at the online USGS river gauge. This will give you a good reference point for future trips. Observe the weather in relation to the gauge for even better future reference.
The advice and opinions on this page are mine only. Everyone has a different style, however this should be enough to get you started. In time you will most certainly develop your own way of doing things.