Safe way to reform high-voltage capacitor
There are a few things I do when powering on circuits if the condition of circuit is unknown:


Visually inspect the circuit, and do a continuity check on the voltage rails to make sure they are not shorted to ground.
I find a way to monitor the current to the supply and estimate the current usage, if I can I find some way to limit the current. If it's an AC device, I use a kill-a-watt meter. 
The best thing you can do is get a hold of a thermal imaging camera and watch hotspots. I turn the supply on momentarily and see where power is being dissipated. Parts usually die thermal deaths. It really depends on the design, but it would be unusual for anything to get above 90C, if anything gets hotter than 120C there is most likely an issue with that part it it should be inspected further. Then increase the amount of time the supply is being turned on for and watch the temps of components. 


If your worried about the old caps, unsolder them from the board and do an ESR test and leakage test