What amount vp ups should I use to Keep my PS4 on for 1 minute?

Solution
I don't get if you want to keep your PS4 running for 1 minute (as your topic title says it) or for 1 hour (as you explain in topic)?

In first case, PS4 has 240W PSU and max what it draws during gaming is 150W. For 150W load on PS4 and TV too (let's say another 100W), a 500VA / 300W UPS will do and you'll get about 2 minutes of runtime out of it. E.g CyberPower SX500G,
specs: https://www.cyberpowersystems.com/product/ups/sx500g/

But if it's the latter then do note that UPS isn't designed to keep electronics in use for longer periods of time (15+ mins). If you need keep your gaming console running for hour or so, you'd be better off buying diesel/gasoline powered generator and transformer.
If you still want UPS then you'd be looking...
I don't get if you want to keep your PS4 running for 1 minute (as your topic title says it) or for 1 hour (as you explain in topic)?

In first case, PS4 has 240W PSU and max what it draws during gaming is 150W. For 150W load on PS4 and TV too (let's say another 100W), a 500VA / 300W UPS will do and you'll get about 2 minutes of runtime out of it. E.g CyberPower SX500G,
specs: https://www.cyberpowersystems.com/product/ups/sx500g/

But if it's the latter then do note that UPS isn't designed to keep electronics in use for longer periods of time (15+ mins). If you need keep your gaming console running for hour or so, you'd be better off buying diesel/gasoline powered generator and transformer.
If you still want UPS then you'd be looking towards 1500VA / 900W UPS and that is for the PS4 alone, no TV power consumption included here. E.g CyperPower BRG1500AVRLCD,
specs: https://www.cyberpowersystems.com/product/ups/brg1500avrlcd/

Add a TV and you're looking towards even more powerful UPS if you want the runtime to be 60 minutes.

Note: if you play online then you'll loose the internet connection regardless if your PS4 and TV are on an UPS or not.
 
Solution
The router and everything else required to connect to the Internet should be connected to the UPS; that way everything will keep on working when there's a power outage. A UPS with additional external battery packs could meet the one hour requirement if the TV isn't a plasma model.
 

You do realize that plugging router to the UPS is pointless since he will loose internet connection either way during blackout?

Sure, the router keeps working but it won't receive any internet connection during blackout.
Only way he won't loose internet connection during blackout is when his ISP has ALL it's proxy servers and switch boxes also on an UPS, which i highly doubt.

Also, since UPSes start from 300VA up to 20.000VA, i don't see you suggesting how powerful UPS he might need for 60mins runtime.
 
It completely depends where you live and if the local power outage also affects ISP's hardware.

Your ISP's hardware is either on a different grid than the rest of the people (e.g emergency services electricity grid) or they have UPSes everywhere (which is very expensive thing to do and maintain).