In addition to what anon said, you can devote yourself to the shrine of any one goddess to guarantee a shrine with a quest from her every floor. If you have a lot of gold, you can also use prayers. Prayer to a shrine gives a small amount of reputation, even those shrines that are questgiving and prayer is free. Moreover, there is no limit per floor; you can easily gain reputation from all shrines, including even shrines in adjacent locations like prisons. If the shrine does not allow you to pray, spend a lil bit mana or WP if it's Restoration, or put on an associated restraint (the size of the reputation gain does not depend on the cost of the prayer, so to save gold, use the low-level ones).