The answer is “any of the above” as it depends on the employer. Some feel they should not waste any time with those who will be removed from consideration if they have a negative background and these check immediately. Others feel that many will not make it to the “ready to make the offer stage” and do the background check then. If you have a negative issue, it will be found and most likely will remove you so do not think you will outsmart them – you won’t.
After the offer. Law requires that criminal background checks can’t be completed pre-offer. It also costs money, and so there’s no point spending the money until they have a final candidate.