Why should people sign up to give money or gear for you doing something many other people do for fun or for the experience?
Are you skimming the first X dollars of contributions to help pay for your expenses, or do you have money budgeted and set aside to pay for your own costs, and all money pledged will go to some charity of your choice?
Is your total budget on the order of $3,000 to pay for food, camping, and emergency shelter, and you figure you can do it with $2,000 and have about $800 to spend on a bike? Does that $800 include racks, bags, tools, spare tubes and other parts, etc.?
Those questions aside, used might be an option if you have a friend who can check it out thoroughly (or room in the budget for a bike shop to go over it with a fine toothed comb). I lean heavily to directing newbies to a local bike shop (LBS) otherwise. A good LBS can help fit you, show you how to fix minor things like flats and shifting adjustments, take care of any unexpected problems that pop up in next spring's training, and give the bike another thorough once-over before you leave.
I think the Fuji is the only new touring bike close to the $800 bogey. Slick tires on a mountain bike gets you about 80% of the benefit of a touring bike -- everything but multiple hand positions. Hybrids are all over the place now; some are re-branded MTBs without offensively lugged tires, some are road bikes without drop bars. So my non-Fuji recommendation would be to find a good LBS, get a solid MTB or hybrid without any suspension "features," preferably with low gearing and mounting points for racks, and start training ASAP. Two or three weeks before you're ready to leave, take the bike in for a checkup or overhaul. In between, collect something(s) to haul the gear.
And have fun, however you do it!