Despite some of the comments here, I suggest that you don’t overthink it; just buy an APC Back-UPS 600VA and be done with it. You have relatively low power requirements. The UPS will provide some surge protection (490J), several minutes of uptime, and a USB connection for automated shutdown.
The 600VA unit is less than $100 USD and replacement batteries are about half that. I’ve been using several of this same model for years without issue and we have many brown/blackouts being in a rural BC community. The batteries have lasted me 4-5 years.
You can always plan for something more significant down the road, if your hardware or needs change, but this should do fine in the interim.
If you want free tier with good privacy practices, Proton is going to be the best option.
I have several paid webhost accounts already, so I just use those for email. Any important messages (which are increasingly rare) are saved to PDF and stored offline (business/tax/medical info, etc.), and the rest is purged once read/sent.