Not sure what you have but a MTB might be fine especially since you are on a budget. Depending on where you live and what airline you use, it may be much cheaper to buy a bike there than to ship one. Definitely check what the airline charges for checking a bike before committing to one.

BTW, when you typed 50-10km a day was that a typo? I have to wonder if you meant 50-100km, if not that is pretty short mileage and you might find the bike choice to be less of an issue. Also you don't mention how much you expect to be carrying. That could be a pretty big factor in the choice.