Bombs are much more valuable when hunting for Secret Rooms as these can provide free items.
Curse Rooms guarantee damage and can lower the chances of Devil Rooms. However, if Isaac has a full Soul Heart, Black Heart, or Bone Heart, the reward can outweigh the damage and still allow Isaac to access a Devil Room. Alternatively, wait to enter the Curse Room until after visiting the Devil Room.
The Bible can be used to instantly win the boss fights against Mom, which can be used to preserve key health, and Mom's Heart/It Lives, which will complete the challenge.