I have always tried to buy cases without power supplies, and then spend a bit more on a quality PSU. If the case I wanted came with a generic power supply, I usually just chucked it and replaced.
Another thing I cannot recommend enough to go with a good PSU, is a UPS system. It's an extra expense, but for ~$60 or so you can get a decent one. It cleans up your local mains, and provides a shock absorber for your PSU, providing protection form surges and brownouts. You don't really need one with unlimited battery backup, just something to ride out momentary events, or give enough time for a smooth shutdown in case of complete power failure.
I have only had one power supply fail in 20 years, and that was the only one not protected by a UPS.
I spent many years in corporate IT, so maybe power backups was just drilled into me, along with good security and backup practices ...