You should be ok. I know a friend had ONE DUI conviction but he still managed to get US citizenship. He even didn't mention his arrest and conviction when interviewed by INS.
I guess this was because those little things were not in the FBI computer by the following possible reasons: 1) FBI was too busy to put those things in. 2)FBI made mistake.
You should learn the lesson, though,and you need to have a lawyer to expunge your record after certain time line set forth by the judge so that you have better chance not only to avoid troubles but also to become US citizen