Is it possible to apply this at the network level? I want to update my home router easily so that all devices in my home can benefit, not just my own laptop (since most of these lists are just updating /etc/hosts)
Yes. Please check pi-hole project [1] or flash your router with open-wrt/dd-wrt and run dnsmasq with the FreeContributor lists.
do people usually do this directly on their FIOS router or is it easier to get a separate wifi router?
https://pi-hole.net/faq/can-i-set-the-pi-hole-to-be-the-dns-...
good stuff