Hey all, and first off this sounds like a kick-ass idea, second, sorry this will be a long post.
I've spent some time on the ol" mississip', but only in the vicinity of Winona, MN, and in the St. Croix river (a tributary and the northern border between MN and WI) It's a pretty calm and beautiful river at both of those points, but I'm not sure what it does elsewhere.
I canoed a long stretch (about 150 miles) of the Wisconsin River (also a tributary) last summer, from Whiting, WI to Merrimac, WI. Between these two points the river is pretty darn wide, approaching the Mississippi in width, and even wider when impounded by dams. My experiences (although somewhat limited) with these wider rivers is that they are pretty tame and predictable. I dealt with some really crazy weather conditions during my trip (high winds right in my face, waves up to three feet tall and whatnot), but I didn't have any "risky" conditions from the river itself.
The Mississippi is a huge thoroughfare for cargo vessels. This would work with, and against you at the same time. On one hand, water levels are carefully controlled with locks and dams to get the cargo to its destination without problems (so pushing yourself out of a swamp is HIGHLY unlikely), but on the other hand, you would be dealing with a lot of traffic. There is a certain etiquette to staying out of large boats path, just like being savvy in a train yard. A lot of traffic will also be recreational/fishing boats, which can vary widely in how "polite" they are to a small boater. Some will slow down and give you a break, others will speed up to create a big wake just to fuck with you. Not something that should discourage you, but something you will probably experience. Something that helped me on my trip was waking up wicked early, like 4 am, and getting on the water before people started showing up. This also helps with rough weather too, as wind is generally the highest at mid-day, so if you can get half a day in by then you can chill and fish or something when it gets shitty.
As far as boat choice goes, this mostly depends on how experienced you are with paddling. I am a canoe fan myself, and love them for how much fucking stuff you can pack in them. A decent aluminum canoe would run you about 150-300 bucks in my experience, and a cheaper plastic canoe could be found for 100 or less. The thing with canoes though is that they keep their value, so its likely that you could sell it for the price you bought it for at the end of your trip. CRAIGSLIST IS YOUR FRIEND.
Kayaks are stupid easy to navigate and generally run lighter in weight than canoes. I would also respectfully disagree with AlmostAlwaysLost and say that in my experience kayaks are more stable than canoes, especially if you haven't had much paddling experience, but they come with the trade off of less gear storage. Also, the fact that kayaks are enclosed makes water really hard to get out of them once it gets in. And it will get in. (Plus, if you get a decent size canoe, like 16-18 feet, you can sleep totally comfortably under them if you prop them up on your paddles, its really awesome actually)
Anyway, this sounds like an epic idea, and I would say its totally doable with some proper planning, like AlmostAlwaysLost said. The mississippi is a great river, you would probably have a fucking great time. I also have lived in Wisconsin for a long time, so if you have anymore general questions on weather, climate or whatever I could give it a shot at an answer.
