you might consider a portable power center (an inverter+batteries) vs a ups. ups's are great for gapless transitons from wall current to battery, but the ones you can find on the shelves at OfficeMax usually have a run time of 30-60 min with a moderate load (eg your modem or ONT and router).
for an alternative, consider portable power centers from companies like Goal Zero and Ego. These run from 150W up to 2kW sustained output at prices of ~$300 for a setup that will deliver 250Wh of power (enough to keep your phone and router going for 5+ hours) to 1kWh-3kWh setups in the $1000 and up range that will run all that, and your TV, and your fridge for the same amount of time, or just your networking gear for 20-30 hours of of continuous operation.
Home Depot is an Ego dealer. REI is a Goal Zero dealer.
Bonus, if you use Ego yard tools, the batteries are compatible with their inverters.