Can marrying a man with a criminal record effect me and my son?

Yes, in some circumstances it can. For example, you may not be able to rent because of your husband's criminal record. Additionally, he may have trouble finding employment or if he has a job, he risks losing it due to any furture criminal history check. Also, he may be prevented from engaging in certain activities with you son, such a coaching in any sports programs, etc. There may well be other considertions. It's up to you to decide.