If it is possible, you should borrow a bike from a friend or family for a few weeks. Make sure the bike is the correct size for you and in good working order - brakes work, tires are inflated to the maximum pressure indicated on the sidewall, etc. Then try riding regularly for a few weeks, gradually increasing the mileage. When you are able to ride more than 40 miles in approximately 3 hours, you will have a good idea if cycling is for you. At that point you will also likely have a feel for if you would prefer a road tourer, a mountain bike, a cross bike, etc. and you might also have a feel for whether you want to splash out on a new bike or a used bike.
The type of bike you will have a preference for will depend upon how long you want to travel - is it a week, a month or a year? Is your traveling restricted to a small geographical area or are you going to travel the world? Will you stick to roads or do you want the option of going off-road?
You are not really giving us enough information to answer your query.
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