Hello , 

As your query is you have your AIR is near about 63000 you are willing to take admission in Anna University as it is a first choice, and you want to know about the counselling procedure to get a good college. As per your rank is concerned I would like to tell you that you don't have to worry you will definitely get a good college all you have to do is to apply for the counselling process but as per your first preference is concerned about Anna University the possibility is quite low because the cut off for Anna University is really high and is about 20000 rank only but still you don't have to worry you have varied options to apply for if you want to know about some other college or their details regarding or you want to know about counselling process, we can help you with that all you have to do is to list your problem in the comment section below. Further, talking about your counselling process you don't have to worry as what I said you will definitely get a nice Engineering College due to the rank through the counselling process. 

I hope your query is solved.

Thank you.