I do not think that you will have a big issue with immigration if you only have 1 DUI. However, they will ask you for the court letter that states that you completed the probation, paid the fines etc. At least thats the case in the state I am in. I also would not think that you will have issues with getting H1 visa because your DUI record doesn't have anything to do with you visa. Don't quote me on this but thats just my opinion. Hope this helps!