Hi,
You can use flyback topology at this power level. You can use a TOPSwitch ->
Welcome To Power Integrations | Power Integrations
You can also use UC384x driving a MOSFET.
You should get a lot of example circuits on the net if you search for flyback.
For variable, you can adjust the duty cycle to get variable output. Or you could have a fixed output voltage and adjust the voltage by using a switching regulator.
The current is not great. Include short-circuit protection in the primary side of things and have a fuse/circuit breaker for protection.
Although not much heat is produced, heatsink the MOSFET/TOPSwitch properly.
Use NTC at the primary to limit inrush current. Be careful about the voltage rating of the capacitors.
Be careful while working with this circuit. When plugged in, it works with high-voltage which can be lethal. Also, make sure, there are resistors across the capacitors to discharge them faster.
Hope this helps.
Tahmid.