Your choice for the caliber, type of weapon, and placement of the Back Up Gun (BUG) is dependant on a few things. Some of these are agency and officer specific due to regulations, restrictions, body type, and assignment.
Due to limitations on weight, size, and uniform, the BUG is not designed to be a replacement for your primary duty weapon. While in theory, a full size gun identical to your duty gun would be ideal, this may not be practical.
If the BUG is coming out, then you are involved in an extremely dangerous situation. You are involved in a situation where the use of deadly force is possible or is immediately justified AND your primary weapon is unusable (you are disarmed, out of ammunition, weapon malfunction, left it locked in the jail section, fell out of your holster, etc.) If you are deploying the BUG, then you are in serious trouble.
Weapon reliability may be a primary concern. You need your BUG and you need it to work with the least amount of problems. You may also want to go with the largest caliber while giving up ammunition capacity as you are may be in a Close Quarter situation. If you are farther away, then distance, cover, disengagement, containment, and communication with additional resources may be a better option.
Reliability, concealment, larger caliber usually means a revolver. Shrouded hammers allow for the gun to not be accidentally cocked in your pocket.
Placement depends on the body type and assignment (uniform restrictions) of the officer. I wont go into placement due to OPSEC issues on an open forum, but consider the most likely scenario that you would be deploying the BUG, consider your body position that you will be in, consider your body type and uniform restrictions, and then place the BUG there.
It is better to carry any gun anywhere in any caliber than not carry one at all, but you may find a choice which is the 51/49% solution.
To support the First Responder with the tactics, training and technology to ensure operational success.