Does the method conform to any strong religious beliefs you have?

Certainly a consideration, if you are a strongly religious person.

Does the method appeal to your sexual partner?

It may be a good idea if you are in a relationship or beginning a relationship, to discuss the choices with your partner before the visit.  If you choose a method that he objects to, then you may not use it consistently.

Do you suffer from PMS, acne or other conditions that certain birth control methods might help?

There is sometimes more to consider than just preventing a pregnancy.  Knowing that a birth control method can also treat other health issues may impact your choice.

How long has this method been available and what are the possible negative side effects?

Some people prefer a method that has a long track record and few, if any side effects.  Other people may be willing to trade side effects for convenience.  Other may want the latest, newly developed option.

Is there a method that will allow me to terminate my menstrual cycle temporarily?

You may want a choice of methods that will allow the convenience of not having a regular period until you want to consider a pregnancy.

Is there an emergency method if my birth control fails?

Be sure to discuss this option as well.

Be clear in stating your needs to the doctor and remember to bring a pad and paper so you can take notes for review.  Also remember that it is very natural for your choices of birth control to change as you age, so you may decide to re-visit and discuss these options again at a later time.