Matching Battery Backup "Waveshape" to the Right Equipment?

Controlio asks: "I see all sorts of battery backups out there, from as low as $100 to the multi-$1000 range. One difference I've noted in battery backups is the 'waveshape' it outputs (stepped sine wave, trapezoid, etc). I've heard different types of outputs are good for different types of equipment, and certain types of equipment can be destroyed by the wrong UPS (motors, etc). So what's the best type of output for different kinds of electronic equipment? I'm looking at what exactly I can backup in my room - from computers to TiVos to a rather large TV, large speaker amp, etc etc etc. Are there any deadly combinations that I need to avoid when making my purchase?"