Provide your flight itinerary as is (into Budapest and out from Amsterdam) and provide hotel reservations in all the cities you are planning to visit (Budapest, Vienna, Prague, Paris, Amsterdam). When submitting your application, just let the visa officer know that you will purchase rail/road tickets later since you are still researching cheaper options.
The visa officer needs to know your specific objectives, both academic or professional, for studying in the United States. Be prepared to explain why it is better to study your specific field in the United States than to study at home. Be ready to say exactly what you will study and for what career your U.S. studies will prepare you. Calmly state your education plans concisely and clearly.
The Student Visa kit describes the process of obtaining an F-1 or M-1 Student Visa and provides you with the USCIS forms needed to apply. However, there are two additional visa categories that may be relevant to someone who is interested in coming to the U.S. to study: the B-1/B-2 Tourist Visa and the J-1 Exchange Visitor Visa. Following the overview of the visa categories in this package you can establish which one is right for you.
The M-1 student visa is for students who enroll in non-academic or "vocational study". Some examples of "vocational study" are mechanical studies, technical studies, cooking classes, a language program, flight school or cosmetology program. Unlike the F-1 visa, the M-1 visa is valid for only one year. Students may apply for cumulative extensions for up to three years.
As you begin to think about funding sources for your educational and living expenses in the United States, remember that you cannot count on working in the United States unless you have been granted a teaching or research assistantship. Immigration regulations are very strict with respect to working while carrying a student visa, and when you submit evidence of your financial resources, you cannot rely on potential income. The income on which you base your application must be assured, and it must be equal to or exceed the costs of the first year of your studies.