A normal UPS can do both and will work fine - it is just inefficient to run the router(s) on it, that is all. But by all means, go for it, especially if your PC and router is next to each other. Even better if the PC is connected with the UPS and can power itself down when a power failure occurs. But have never really used that function in any of my setups. At work the UPS simply carries the PCs while we wait for the generator, and at home, I am always there and turn off the PC before or when loadshedding kicks in.
Personally I prefer the split setup, as the mini ups was set and forget. I have not touched mine since I installed it last year. With my UPS setup, I need to cuddle and actively manage it etc. as I hacked some extra batteries into it so that it will last throughout a loadshedding event. So checking that I do not overload it (the wife once inadvertently plugged in the iron!), checking the battery levels (you also need to do this with a non-hacked UPS, as drawing down the batteries below 50% will degrade your batteries within months), checking the heat output, cooling it etc is an active mission. Sure, a 2000VA UPS will probably work in your case, but it all depends on your server. If it aint a beast that will chow your whole battery capacity while it is shutting down, then by all means, get one like that, to power the whole setup.
Sorry if I cannot recall/have missed it, but what are you trying to power, and for how long? A 8800mah gizzu will withstand a 4 hour loadshedding without even trying.