check these links:
http://www.bikekatytrail.com/
http://mostateparks.com/park/katy-trail-state-park
I live in Jefferson City and ride the sections east and west of us pretty extensively.
West of Rocheport the trail is largely away from the river and out in the open. From Rocheport east the trail is in the Missouri River bottoms and is at times sandwiched between the river and the bluffs. Generally lots of shade along the trail due to the canopy of trees. Surface is crushed stone and generally pretty smooth unless it is a freshly repaired section which may have some larger gravel mixed in. I run Continental Travel Contacts in a 38 width on my Tricross. Anything bigger is not really needed but 23-25 road tires are too wimpy. Anywhere in between and you should be fine. Be aware of rolling off the trail surface, in sections the honey locust trees and their wicked thorns will do a number on your tires. There is also plenty of poison ivy along the sides of the trail but does not need to be a problem since the trail is 10 feet wide or so. There's plenty of room to ride side by side as long as you aren't meeting oncoming riders, then its the normal drill of dropping back single file until clear. Same way with passing slower riders - simply call "on your left". You will encounter, especially if its a weekend, recreational (using the term pretty loosely) riders who don't understand these riding rules so a smile and a little patience goes a long way with them. But most of the time you will have long stretches of solitude.
The links above will give you a pretty comprehensive list of food, water, lodging/camping resources. At Jefferson City, you can take a spur trail from the Katy trailhead and cross the river and ride into town. There is a great bike shop - Red Wheel - just a few blocks down from where you cross the river into town if you need repairs or bike supplies.
Each trailhead location generally has water and restrooms, some have bike tools and air available also.
The Katy is a great rail-to-trail conversion, and if the proposed Rock Island Line gets converted, would give us almost 500 miles of connected rail-to-trail riding. How cool would that be. If you have any other specific questions I would be glad to try and answer for you.