You could, however, try to find an employer who_s willing to submit H1B visa petition on your behalf. H1B is valid up to 3 years and you may renew it once more (for another 3 years). Once you_re employed and if they deem you valuable enough, they might be willing to sponsor a greencard for you. I know this is possible because a friend of mine who has a Master Degree in pharmaceutical was lucky enough to find an employer to sponsor her work visa. A year later, they approached her and let her know they_re willing to start the green card application process.
Your best option is to get a student visa and see how you like it in the U.S. If you decide you like America and want to stay here and get a job, you would need to apply for a work visa. You have to have a job with an employer to vouch for you before you can do this. Once you have the visa, as long as you keep it up to date, you can stay for as long as you would like or as long as the terms of the visa allow (it differs with every person). However, I would suggest that after a few years, apply for a green card. You would have established a good record in the U.S. and paid taxes so getting one shouldn_t be an issue. After several years, you can become at citizen!