Yes, for me personally constant software updates are a huge deciding factor. If a device comes from a manufacturer that has a history of dropping support for their routers after 1-2 years, I wouldn't buy their product. All too often the routers out there run for years without any updates, all while new issues appear constantly. For example, the KRACK vulnerability that occurred in 2017 left thousands of unpatched routers with glaring WiFi vulnerabilities. Let alone the tons of other vulnerabilities that plague residential routers.
Because of that reason, I personally like to suggest Ubiquiti's Edgerouter X router paired with a Unifi wifi access point for tech-savvy users. Ubiquiti provides firmware and security updates all the time, and the router itself offers tons of enterprise-level features for a bare minimum price. It also comes with a great GUI and setup wizards, so you don't have to be a crazy network geek to figure it out!
If you're looking for a simpler option, Ubiquiti also makes a simpler plug-and-play system called Amplifi. This system also gets lots of updates from Ubiquiti, while also having a super user-friendly interface. While I am personally a huge fan of Ubiquiti's products, I've helped others use the popular Netgear Nighthawk router with great success.
Based on my experience, most newer routers out there in 2019 seem to be pretty decent. In terms of routers to avoid, I would suggest being suspicious of mesh WiFi systems. As mentioned above, your mileage may vary. If you live in the middle of nowhere, those systems work pretty well. If you live in a urban apartment building, your experience will be pretty mediocre, as WiFi signals will just interfere with your neighbor's, and in the end nobody wins. Nothing beats a hardwired connection to a device in those cases.
Out of curiosity, what is your reasoning for using your own router? Are you looking for better network performance, or more just to remove the rental fee? Your intended usage would determine the best router to get.
If you don't use the FiOS branded router, some service will be impacted such as caller ID on screen, and remote DVR. On demand and guide services can still work! You'll need a plug-and-play device called a MoCA Bridge. This device bridges your internet connection from your router, and sends the connection over coax cable. This allows your TV boxes to access the Internet, and access On Demand and TV Guide. They can be pretty expensive as standalone devices, so another option if you're feeling crafty is to pick up an old Verizon Aciontec router (you can find them for cheap on ebay, $10 or so), and use this guide to set it up to act as a MoCA bridge. I've done this setup for at least a dozen home FiOS users with FiOS tv without issues for years.
Also, the ability to mange your WiFi password and such from the Verizon website would also no longer work. Otherwise however, FiOS services shouldn't be impacted (such as phone).
Please do let me know if you have any other questions!
Thanks for asking!