So a new company you are joining can easily verify your current salary with your ssn & dob. Right? They have your history of employers from your resume already.
Get the job offer and negotiate salary before agreeing to a background check. Let them make the offer be contingent on the results of those checks (and drug screen or security check or whatever else they want).
But before turning in notice on your current job, wait until all checks are completed and make them reissue the offer letter with all contingencies removed. Otherwise you're still at risk of them pulling the offer while you're busy packing up your desk.
