I agree with the recommendation if a mountain bike if you are a newbie.  Whilst the trail is mostly fire roads a mountain bike will feel much more stable and will cost less.

The less gear you have the easier it is on hills an on the few single track/rugged sections.  I toured with two panniers which were fine however I did try to keep them light.   I had a two sets of bike gear, full rain gear, a warm sleeping bag, a book, descent camera, long johns etc, a change of clothes for off the bike and jandals as 2nd footwear.  Shared was a gas cooker,  basic cooking gear and a water filter.  Given we were in tour mode the panniers were fine.  Get quality that clip on well.  Ortlieb are great.

Alternatively you can go bike pack style and go minimalist.  It is  trade off for creature comforts.  Seat bags & frame bags handle getting bounced about much better than panniers.  That said there isn't much bumpy stuff to be encountered.  I would stay away from trailers.  At high speed they can get the speed wobbles.  If you have to hike up hill they are a major drag.

As far as shoes go, I recommend a cross shoe which has some flex. These are much more comfortable to walk in around camp and in towns than a stiff mountain bike shoe.

Check out crazyguyonabike.com  You will find lots of blogs of riders touring the divide.

Enjoy :-)