What is the best way to be notified when my power goes out?

We lose power quite often. Unfortunately, we have an extremely-necessary sump pump. I’ll leave all discussions about battery backup and auto-start generators out of this thread. This is because I have a specific need for the following:

When the power goes out, I want to immediately be notified. Ideally, notification would come in the format of an email or text, but a phone call of some kind would be fine.

I was originally thinking that the following would be my best option:
Plug in and configure an old Android phone I have kicking around to send me a text message or email when AC power has been lost. This can be done fairly easy with Tasker (app). The catch would be that this phone would not have phone service. It would be dependent on wifi to send this text message or email. So, this means that I would need to buy a UPS battery backup and plug my wifi router into it. I believe this would work. But I’m somewhat concerned about the fragility of such an old Android phone and the potential for possibly putting wifi into sleep or some crap. The other concern would just be having that thing plugged in all the time. But it might be worth a try.

Another option would be this. I have no experience with this device, but it seems like it would do the trick. Has anyone ever tried one of these? It seems that I could simply plug it in next to a phone jack and it would place a call to me when the power went out. Now, I have Verizon FIOS phone service (VOIP), but the install includes a battery backup that allows for about 6 hours of phone use when power is out.
The advantage of the Reliance device would be that I could avoid the purchase of a UPS. But the Reliance is more expensive than an inexpensive UPS. Plus, the Reliance seems to only call (not ideal) after 5 minutes of no power. I want immediate notification.

Anyway, if anyone has any other ideas or experience with one of the above, I’d love to hear your thoughts.
Thanks.