First, square wave won't damage anything over the few minutes it will be in use in the event of a power failure. Sine wave is better if the price works, but it will always be more expensive.
Second, don't get confused between W and VA. A 1500VA UPS does not provide 1500W of backup power. I have in this room two 1500VA units that supply up to 865W of power and one 1500VA unit that supplies up to 980W. At my office, I have two 1500VA units that supply 1440W each. The difference is battery voltage - 24V, 36V, and 48V nominal, respectively. So if you don't see power capacity explicitly listed, look for battery voltage - the higher the voltage, the higher the capacity.
I agree that line interactive with AVR is much better than standby. In the event of over or under voltage, a standby unit either does nothing, or switches to battery, so you're discharing and charging constantly for the duration of the out-of-bounds power situation. That shortens the life of the battery significantly. AVR in a line interactive unit uses transformers to boost low voltage or reduce high voltage, without touching the battery. If the variation is too high, such units will all fall back to the battery. The specs should show how much they can handle before doing that.
A UPS described as "online" is the best way to get very clean power for sensitive equipment, as the incoming AC power is converted to DC, then back to AC, which makes the output absolutely consistent. Such units are quite expensive, and completely overkill for a computer. The switching power supplies found in PC's can handle quite a lot of input variation - almost all currently sold can operate at any value between 100V and 240V (and work more efficiently at higher voltages).
Given where you're posting this question, it's a safe bet the UPS is for a gaming machine. Given that, I'd recommend jumping straight to a 1500VA unit, which won't shut down in a panic a few seconds after the power goes out should you happen to be in a game sucking up a lot of juice. That also gives you spare capacity to plug in things like a router, switch, cable modem, etc.
The brands I'd recommend, in order, are Tripp-Lite, APC, and then CyberPower. That's pretty much descending price order as well, for roughly feature-equivalent units. Make sure whatever you get has user-replaceable batteries, and be prepared to replace them in about three years. You do not want to think you're safe only to have the UPS quit immediately after the power fails because the battery is shot.