It's really not too easy, I know having spent many hours trying to do it (switched to other projects, will return to it).
The best advice I can give is buy a PS matching those specs from China. Although, do look inside before installing it.
Otherwise, this is what you do:
1. In Digikey parametric search choose your controller. Many have built-in power MOSFET but I think with your power requirement you may have to use an external MOSFET.
2. Design your transformer, I used a procedure from a book and wrote a Python program to carry it out. It involves basically figuring out how much energy the transformer needs to store and your maximum DC resistance and so on, then choosing a bobbin, core and wire of sufficient capacity.
3. Read datasheet for controller carefully and build one of the examples in it. It will help you calculate resistors etc.
4. Pay particular attention to the feedback network. This is rather tricky as it has an opto-isolator driven in its linear region. There is a part that is used for this, something like a buffered reference with error amplifier or similar. Being clever I tried to make do with a less complicated circuit. Bad!
5. The SMPS IC and the feedback IC will have to be compensated, since there is delay through the loop and without feedback it will oscillate. In your application you can tolerate slow response to step-changes in input voltage or load conditions, so be generous with the compensation. Otherwise it's tricky and perhaps best done by experiment, as I don't know of a good mathematical procedure so far.
Still keen? Keep us posted
cheers, Nick