Done the Mississipi from St. Paul to New Orleans a dozen times as a deckhand on towboats. Would not do that river in anything but a hard bottomed boat under considerable power. Would rather do Class 5 rapids. You will not be able to row yourself out of trouble. The tows are huge, particularly on the lower river: up to 8 acres. Think the equivalent of (10) 100 boxcar railroad trains. Think 8 or 10 ocean going freighters. Going downstream they cannot stop for miles. They have enormous suction and could pull a raft or skiff under. And swamp big boats in their wake. The towboats have up to 25,000 horsepower and they call the propellers wheels as they can be ten feet in diameter and more. The housing around the propellers is designed to have a kind of jet engine type propulsion. The river pilots cannot see you. The natural river currents are powerful and can pop a 40 foot log up into you at any time. Do not even think about going on the river anywhere near flood stage. I can remember 20 mile an hour currents.
That being said, the upper river is gorgeous with beautiful bluffs and wooded hills and islands. But there are 27 locks and dams that bring slack water and long waits to lock through. The commercial traffic has the right of way. You will need a radio to communicate with the lockmasters. Powerful currents as you exit the locks. The lower river below the confluence with the Ohio River is an unseemly ditch flanked with high levees over which you will not be able to see. The river is fully 3 miles wide just below the Ohio! It is the only major river in the world that narrows towards its mouth - 1/2 mile wide at New Orleans. And 180 feet deep!
For 20 to 30 miles below cities the river is grossly polluted. (The cities do not treat raw sewage after a heavy rain). The river does seem, read seem, to clean itself up after a score of miles or so. There are places to camp on the upper but on the lower hardly anywhere. Think lots of insects. The Mayflys in May and June are so thick on the upper river the municipalities bring out the snow plows to clear the bridges.
The upper river between Lake Itaska and St. Paul might be the best bet.
I admire your ambition. People do it but people also die trying.