UPS devices are rated with "VA" and "Watts" as well as a run time at full power. The VA is an annoying number that is only useful when comparing UPS against each other when you don't already know what you need. The watts is the maximum power your UPS will support when power goes out. So take your computer's power supply (say, 600W) and your monitor's power supply (say 200W) and you should get a supply that will support at least 900 watts. After that, check the supply's run time at full power and choose one that gives you enough time to exit your game, save your files, and turn the computer off. 2-5 minutes at a given maximum wattage is normal.
Here's where it gets sticky. They are generally considered "emergency" backups. If you use one to its full capacity and drain it until it shuts off, you've almost certainly damaged the battery. The lead acid batteries aren't happy if they're every discharged below 50%. On top of that, even under normal usage they will degrade and you should expect to replace the battery (or whole UPS) every 2-5 years. Because of the first issue, you might want to get a supply that has double the capacity if you want to use the UPS frequently.
If you are also dealing with brownouts, surges, or other power problems and frequently have electronic devices die due to power issues, you might want to look into "online" UPS supplies, vs "offline". Online means they are always powering your computer with the converter, supplying a constant source of good power directly from their inverter regardless of the AC power coming in. Offline means that the converter is inactive until the power goes out - in other words they just connect the computer to the powerline as long as there's power, and then switch to the converter when the power goes out. The online UPS supplies therefore absorb any brownouts, surges, and other electrical problems and your computers never see any of that. Good offline UPS supplies also provide some amount of filtering and protection, but eventually such protection wears out, and isn't as bulletproof as a good online converter.
The cost difference is very high, though, so I wouldn't recommend it unless you know your AC supply is terrible.
Beyond that, make sure you test frequently once you have one. And not just using the "test" button, but actually unplugging it and making sure it'll power your system for the several minutes you need. Otherwise you're going to be caught short when the power goes out and you didn't realize the UPS was in bad condition.