Well, being completely honest have a record would make it much more likely you would not be approved, depending on what the offense was for. However, everyone makes mistakes but it will sure add to the scrutiny you will receive.
It is also common for many to come believing they already know all the secrets forms of recognition only to learn they have been dooped by web sites thinking they know the truth. Disinformation at it's best.
The best thing I can suggest is to look in your local phone book and find a lodge near you. Find out the night they meet and go there early and speak with some of the Brothers. Be completely honest, as they will find out and see what happens. Best of luck and don't hesitate to ask if you have any further questions.