How to set up a solar powered wifi backup

I don’t know if this is the place to ask this but I’m looking for advice on how to add a solar backup to my modem and router.

I live in a house with no cell service and high winds unfortunately mean we occasionally lose power.

I signed up for a second internet service because they occasionally go down even when power is still active. I’m hoping to connect the modem and router from the second internet company directly to a solar panel but I don’t totally understand the process. Ideally, I’d like something that runs on the house’s power and then switches over to solar in the event of an outage, but I don’t know if that’s possible.

There’s a 100 watt panel available at harbor freight for $ 120. From what I understand That’s more than enough to power the two devices… But I don’t know if I have to consider more than just the power that they use, but also whatever battery is needed?.

I’m also not sure what kind of battery setup is needed for this to work. Would this be something I hook into a UPS? So the solar would essentially power the UPS all day long and then after dark it would go to battery backup for hopefully a few hours. Is there a battery that’s available that would last for longer than a few hours? Would everything just power on in the morning when the sun’s out?

If there’s some kind of rudimentary guide to getting started with a project like this, or if people have tips on products or things to avoid, I’d love to hear it!