Once one told me that having a low-wattage UPS would make useless my PC's trillion-watts bad-ass PSU. Is this true? Is this true even for normal plugged usage?
The UPS doesn't affect anything unless you have a power condition (power loss or brownout) that requires your computer to use its power. The power rating of the UPS defines how much power you can pull from it without damaging the UPS. If you try to pull more power than it's rated for, it will pop an internal breaker on most UPSs to prevent destroying it. In that case, it serves no purpose other than providing some surge protection because you lose power anyway.
You mainly use a UPS to provide power long enough to shut down gracefully. The internal battery capacity (its amp-hour rating), determines how long it can provide power. So rated run time is also an important specification to consider when you size a UPS. Run time is related to the load of your system. Whatever run time the battery will provide at its full rated load, it will be longer if the UPS is supporting a lesser load. So getting a UPS with a higher power rating will often give you more run time. This is not a hard and fast rule, because a higher-capacity UPS could actually have a smaller battery. However, if you look at the run time spec for a higher-capacity UPS, you can expect longer run time than the stated full-load run time if your system uses less power.