Hello to anyone who sees this post.  I realize that Marković is possibly one of the most common Serbian surnames, but I am trying to get some advice in my search to find out more about my family history.

My grandparents have died a long time ago, and I fear that part of my family story has died with them.  I am looking for any record of the following:

• Birth records of Grandparents
• Marriage Records of Grandparents
• Imprisonment Records of Grandfather (political dissident, potential prisoner of war in ww2)
• Birth records of My Father and his siblings

For Both of my grandparents, the only thing that I have beside pictures, is an arrival card (arrival to NYC, United states). The arrival Card has the following information on it, but i am not sure how accurate the arrival cards are for dates and spellings:

Grandfather:

Name: Milos Markovic

Birthdate: August 9, 1908

Birthplace: Dobrodo, Uzice

Grandmother:

Name: Milanka Markovic (Starcevic)

Birthdate: January 24, 1926

Birthplace: Gostinica, Uzice

Where would be a good place to start my search for information about my grandparents?

Also, My father does not have any records of his birth or remember where in Serbia he was born. He and his parents fled the country as refugees when he was around 8 years old. Where might I try to find a birth record? 

Any advice would be greatly appreciated. My father and I hope to learn more about our Serbian heritage. We hope to travel to Serbia as well sometime in the future.