Yes, you should have a UPS. Always. Whether your house a month old or a century old.
An older house might be a problem because it was around 1970 that US codes required grounded (three prong) outlets. I'm not sure if any UPS systems work on ungrounded (two prong) outlets. An electrician could probably put a grounded outlet in your computer room for a reasonable sum.
UPS systems are typically rated in VA, not watts. 1000 VA is about right for a cMP, although you also need to add margin for the monitor, external drives and networking.
Note that you shouldn't plug a power strip with surge protection into a UPS.
Where is the power factor? Volt-Amps x Power Factor = Watts
Lets take account of only the power factor versus the full rated capacity (980W) of a MP5,1 power supply, not even take into account the over capacity needed to counteract initial spikes and other peripherals.
The formula is: A = (Va * Pf)/V [with the optimistic Pf of 0,65]
VA * Pf = W
VA * 0,65 = 980
VA = 980 / 0.65 = ~1507,7 VA
So, your suggested 1000VA UPS will be enough for a consumption of only 650W, and this is not taking into account the at least 20~25% safety margin that you need to have. A basic single Xeon MP5,1 without any upgrades will probably fit into this envelope, but any MP5,1 with a 130W Xeon, all SATA bays used and with a current GPU like RX 580 will easily top this when in full usage.