If your objective is to turn on the PC with a command by the microcontroller then,
Instead of putting the realy at the output of smps(ie switching the supply to motherboard and other peripherals), you can control those ON signal of the smps.
means,when manually you press the start button on the pc, two wires are shorted during that switch action.
Put a relay at that point. ie, instead of shorting those to points manually with the ON button, you are going to do it with a relay and the SMPS turns on.
This would reduce the current rating of the relay, as you are only switching the signal line and not the output line of smps as you mentioned.
In this case a very low rated relay should be fine. look for
Current rating - 1A
Coil Rating - 5VDC
Contacts - SPST,SPDT
(Make: OEN/GOODSKY/LEONE)
Controller too can be a basic one. Look into
www.microchip.com for PIC controllers.
cheers!