Marriage base green card-asylum case pending CHICAGO IL

[TicTac]

I came in US on J1 visa. Then I submitted application for asylum and the case is still pending. Meanwhile I met my fiancee and we are getting married next month. But we are not sure if I should stop my asylum case. Is there anybody with similar situation?
Any suggestions? He is a US citizen. We are going to file in Chicago. And btw how much did you wait to be called for the interview and after that to receive a GC?
Thanks everyone for answers in advance!