Despite making a choice, it is not final until you activate the bed, and therefore going back to the statue of Mara and reactivating it will allow you to change the decision, which can be useful to get lockpicks as if you ask to escape, you will be given lockpicks and then you may change your mind but will still have the lockpicks. Once chosen, the Dragonborn must sleep in the bed and their new life will begin.
All races other than Wood Elf get special options unique to their race. In it is a statue of Mara that, if talked to, will ask them how their new life shall begin. The Dragonborn starts off in a cell in the Abandoned Prison.