performance metrics for power supplies (a PSU as opposed to a UPS) are calculated using the regional AC sine. anything other than a pure sine is going to make the connected PSU work harder and, eventually, marginal components may fail.
having said that, stepped square, modified square, simulated sine are generally going to be perfectly fine for virtually any consumer equipment you connect to it.
cyberpower make cheap (but halfway decent) UPS units. I have used both APC and cyberpower for years without issue.