That's interesting. I didn't know routers kept logs. Did
you find that by logging in to the "control panel"?
I used to get a lot of attempts to get into my computer
when I had dialup. That mostly stopped with cable, though
I have caught my cable company, RCN, trying to get
in. I have no idea why. Apparently they just go around
snooping on customers, perhaps tracking how many
machines are at each address, or some such.
First, do you have a good, long password for
your router? You should. Maybe 20 characters.
You didn't mention what computers you have.
Assuming Windows...
It's important to understand that most
Windows computers are full of holes. The default
configuration has numerous unsafe services running.
Many people now also enable remote Desktop
functionality for tech support. You should have a
firewall that blocks all incoming and asks permission
for all outgoing processes. (In many cases it's also
possible to block svchost from going out, which takes
care of most or all Microsoft spyware.)
Some may remember there was a problem with XP
in the early days. A service called Messenger (not
Windows Messenger) was running by default. It was
intended for sys admin people in corporations to be
able to pop up notices to employees on the network.
(Like "Don't forget: Company picnic on Saturday.")
It was being used to show people ads. The problem is
that Windows NT (2000/XP/Vista/7/8/10) is designed
to be a corporate workstation. It's a sieve, set up
with the assumption that the network is safe while
the users can't be trusted. If you want to set up
reasonable security see here:
http://www.blackviper.com/
You can use that site to adjust services. And get a
firewall.
I don't know much about Playstation, but that's
a good example of increasing intrusion online. Online
services and spyware operating systems are changing
the norm. Most software is now designed to call home
without asking. A few years ago that was known as
spyware. Windows 10 is a new level of spyware. It
now has a privacy policy and TOS that claim Microsoft
has a legal right to spy on virtually everything you do.
(I suspect Playstation is probably worse in that regard.)
At the same time, more people want more of those
services. Without selling out to Apple you can't get
all those nifty apps. Without selling out to Adobe you
can no longer use Photoshop without it spying on you.
The latest version is still installed on your computer,
but it's officially marketed as an online service. The
difference is not so much in the software but in the
fact that you have to accept it as spyware. MS Office
and many other programs are going the same way.
They want to steal your car and rent you a taxi.
So there may be different, conflicting concerns
for you. One concern is preventing malware/spyware
intrusion by strengthening your security. But then
there's also the issue of whether you're actually willing
and able to do that in the context of how you want
to use your connected devices. If you want to accept
and use online services then you must accept that
you're now in a shopping mall. The mall cameras,
marketing data collectors and security guards will be
watching. You're on their property, not your own.