I'm by no means an expert, but I know it depends a lot on your criteria. For example, will you be transporting the bike by train, plane, or car? If so, look for a folding bike or at least one that disassembles easily. If you're going to travel by bike the entire time and not by other conveyances, and if you'll stick to paved roads, then a road bike (skinny tires, smooth tread) may be best. If you prefer a more upright sitting position, then try out a "comfort" bike. If you'll be doing off-road traveling, try a mountain bike. And, there are other categories besides...
Define your criteria, the mission you want to do exactly. What road conditions will you encounter? How steep are the grades? How many miles per day? Then talk to bike experts. Don't talk to just one, because there are different opinions, and some may be trying to sell you something. Try to get the big picture before you buy.
The journey is more important than the destination.