I'm 220 lbs and have done the KATY end to end the last 3 years. I ride on 700x32 tires, but I'm riding unloaded. I can't remember the brand, but they are pretty smooth. You don't need much in the way of tread on the KATY. There were very few people getting flats on the ride, so belted protection for the Katy isn't a necessity; however, you're going to ride it elsewhere.
I'll probably be buying new tires before next spring so the answers of others will interest me.
If you can wait until June, I highly recommend this group. Below is the info for 2013. In 2014 we will be starting from St. Chuck and heading towards Clinton. Of course this group is only going one way, but that wouldn't stop you from riding back on your own.
Signups are suppose to begin on March 1, 2014. Last year the ride filled up in 4 days.
http://mostateparks.com/2013-katy-trail-ride
Oh! Don't forget to do the relatively new part from St. Charles to Machens.