Where are you located? Close to an Eddies or Performance shop?
A road bike is going to be the easiest to ride on that event's course...once you get yourself in reasonable condition and accustomed to the various riding positions it offers.
A road bike offers the optimum positions for aerodynamics, application of power and endurance. It does NOT provide the highest level of comfort. That's where training miles, a properly fitted bike and good cycling clothes come into the picture.
The route they have chosen does have lots of climbing (as you are probably well aware, Ohio ain't flat with the exception of Hancock County!) and the prevailing winds here can be brutal.
You will see folks riding hybrid and mountain bikes on your ride. They will be working a bit harder to propel their heavier bikes up the hills and the more upright riding positions also take more energy to get them thru the air.
Hit a decent local bike shop and discuss your experience level, your budget and cycling goals. They will get you pointed in the right direction, bikewise. Test ride a few bikes if possible. Talk about a triple crankset or a compact crankset for lower gearing. Both provide lower gear ratios over a standard 39-53 crankset to make climbing those long and steep hills a bit easier.
Discuss slightly wider tires for a bit more comfort, if you think you need it. Try sitting and riding on several seats if you can. Finding 'your' seat can be easy or it can take years of trial and error.
Find out the 'must have' accessories you wil need for your big ride around Ohio...a patch kit, a couple or spare inner tubes, a CO2 inflator, tire pump and perhaps a spoke wrench and a multi-tool. Any bike shop will take a few minutes to show you how to use your tools and how to repair a flat tire. Basic on-the-road maintenance is your responsibility and it's fun learning how to do it yourself (assuming you can not at this point). You will want a smallish saddle bag to store this stuff in.
You'll need a couple pairs of basic cycling shorts, a helmet and I recommend padded cycling gloves. A jersey is not necessary, it's not faster than riding in a T-shirt, but the front zipper will be appreciated on hot days and the rear pockets become a cyclists best stash spot for food, cell phones, etc. A cheap rain jacket and maybe a pair of cycling tights for cool or wet weather might be something to think about...you know Ohio weather!
Learn how to eat on the bike and about staying hydrated. This June was absolutely a killer to ride thru, even for experienced racers and tourists. Stock up on energy gels and bars for your jersey pockets.
One other piece of advice I would offer you is to get in contact with one or more of your local cycling clubs. Nothing makes learning and training easier as having real, live folks at your side to help you along and give to instant advice if needed. Riding in a group is more fun for most folks and it is safer.
Lastly, ENJOY yourself on the ride. It's for a great cause!
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