Do you have a budget for the tour?
There are some low end touring bikes that work well, like REI .
A roadified MTB or better still an MTB wheeled touring bike will handle rougher trails more easily, but regular touring bikes can be ridden on trails.Sometimes 2nd hand bikes make good buys.
Whatever style or budget, get a bike the correct size.
Keep it simple, because things will break and wear out. Friction gear changers will keep on going regardless, but index only systems may foul up. Dont skimp on luggage, this will take a beating.
For preparation, you need saddle time, rather than any strength or aerobic training. A week into the tour you will be much fiitter, but your butt needs to adapt to the new stress. Better do that before you start. Pick a saddle you can live with, they are all different and many will not fit your butt.
Do a shakedown tour over a weekend or week, to test out your rig. Even riding in a big circle to camp in your back yard is a good test.
There are some things which are essential, like bike shorts, gloves and helmet, there are highly desirable things like wicking bike jersies, breathable waterproofs and stiff shoes/lightweight boots, and there are things which will help you be more efficient, but you can do without, like clipless pedals. You dont need to buy top of the range for things to work.
Check out some of the "ultralight" camping web sites( not neccessarily with a bike) . The ultra-light movement has an interesting take on weight/speed/safety.
Michael