Just as well I don't use "non-branded" PSUs anymore lol.
When I was on a tight budget I just used the "non-branded" PSU that came with my "non-branded" case and the PC refused to boot. Turns out I needed to buy another PSU that could supply more amps on one of the voltage rails. The maximum amp values on the voltage rails is more important than the maximum wattage of the PSU. Post what CPU, GPU etc. and price range you're looking at and maybe we can suggest a suitable power supply.