Lets start with a reality check:
Often the market you are in will dictate the price point, for example: If you are building a product for the PC or PC peripheral market, you are going to need an inexpensive power supply in order to compete.
If you are building a product for the server market, you will need a reliable power supply in order to provide high "availability". Redundancy should be considered also.
Often the power supply has to be the last thing to be specified. If all the other factors are accounted for, the power supply could be one factor that determines when you go to market. See "Custom or Standard".
Now lets begin:
Start with your mechanical considerations.
Is space a premium? It is best to start with the most space you could possibly allow, then when you find a "safe" supply that could fit the package continue to look for smaller package options. Usually the smaller the package the more advanced it has to be and the more expensive it will be. Do you have any unusual mounting considerations? Will the power supply need to sustain high shock of vibration?
What is the thermal environment of the power supply? Ambient temperature & temperature rise within the product. What options do you have to keep the power supply running within its intended operating range. No airflow, convection airflow, forced airflow. Conduction?
DC input or AC Input. What is the desired range of the input? If it is Switching AC input model, the approval agencies may eventually require you to have harmonic correction. If a linear power supply will fit the specifications you desire, you will not be able to use the same model for worldwide input. How many output voltages are required? How tightly do they have to be regulated? What is the duty cycle of each output and how do they relate to each other? What is the output peak requirement for each output and for what duration?
Logic & Controls:
What signals do you require from the power supply such as "power good/fail"? What signals do you want to send to the power supply such as "Remote Enable" or "Margin"? Do you need a voltage adjustment pot or remote sense on one or more outputs? Do you need "Standby Voltage" to keep a processor idle until called upon to "wake up" by the operator?
If your product is to eventually be sold in Europe, you will want to consider the CE mark. If it is only going to remain in the United States, you can probably do with the appropriate UL mark.
Custom or Standard - General guideline:
Here are a few examples that may warrant a custom power supply. You require an extremely cost effective solution for a high volume application, or you require a power supply with features that are not readily available "off the shelf".
A custom power supply will take 12-18 weeks from concept to delivery of "beta" units. Custom units will require engineering fees for design and agency approvals. Custom units do not have the luxury of a proven track record, this makes choosing a manufacturer even more important. Be prepared to work very closely with the manufacturer.
Alternative to custom: Value Added Reseller (VAR)
A power supply VAR may be an alternate solution that is best for your application. VAR's can configure an off the shelf power supply to meet your requirements. Both electrical and mechanical portions of the power supply are enhanced to meet your needs while retaining the integrity of a proven supply. Smaller engineering fees are required, and some designs are ready in 4 weeks.
2nd Alternative to custom: Modified standard
Modified standards are a good alternative when you find a power supply that has a most of the requirements you desire, but lacks in one portion of the spec. Less than half of the powers supply manufacturers are good choices to consider for modified standard. It requires a strong engineering staff and a strong knowledge of the power supply circuit characteristics. The beauty of modified standards is that they can give you a custom fit for a standard price. In many cases there is minimal or no agency costs. Additionally, some manufacturers will amortize the cost over a blanket order.