Not that I'm paranoid in any way, but I only had a single socket at my front door where the main BT line comes in.
I use an old(er) UPS which then feeds an extension lead to feed the modem / router / wireless phone base station.
I do live in a village and my property is fed by overhead lines and although it's been stable of late, we do suffer from a number of power outages a year (once a weekly occurrence and nearly every time it rained. Much better since they replaced all the overhead lines).
My modem/router hasn't been powered down since Nov 13 when it was 1st installed bar one day when my middle son decided to see just what 'that red button' actually did.
(It's had a few manual resets in that time though).

I'd recommend a decent 2-way socket, feeding two extension leads. One for modem/router/phone and the other extension lead for non-phone/network equipment.
UPS is handy if you can pick up a cheap one, but not essential by any means.

Alternative option: the Ethernet cable between the modem and the router can be up to 100 metres long so only the modem would have to be in a power socket by the master socket.