Consumer routers sit at the edge of the home network and are important for maintaining network security. Many of today's unsecured networked devices (IP Cameras, thermostats, etc. etc.) would pose far more of a security threat if they were accessible from the internet. It is, therefore, important to have as secure a router as possible.
Unfortunately, most consumer (and even some business) routers are insecure be default, or insecure due to delayed patches. A great option to improve security is to use the Lede Project router firmware. Get one of the supported routers with decent Ram and Flash to allow customization and upgrades later.
By default Lede installs with a plain old HTTP interface. To reduce the attack surface on the Router, install "luci-ssl" package via System->Packages page. Then restart the utthpd service via System->Startup page.
Remember to keep the firmware up to date. The Lede project has been fairly fast in getting security patches out so far. I hope that continues and improves in the future.