Okay, I see the point of what you're trying to do here. I do. In fact, the instinct you have here does have a core of value in it: if I'm an attacker who wants to do a good old, no-user-interaction-needed-whatsoever breach into your home network by taking advantage of some unpatched security vulnerability in your Netgear router, putting another router behind it that would not be subject to that same vulnerability might well mean that my use of that attack to breach your network. Notice use of the word "might" there; if the second router blocking path has its own vulnerabilities that I can use to get past it then that second router becomes as valueless as the first, and I'm in your network and my mission is accomplished. But, that being said, if your second router is not susceptible to the same attack that broke through the first--meaning it uses a different type of firmware of a different design than your other does-- and if that second router doesn't have its own vulnerabilities that can allow an attacker from the Internet to take control of it or sneak traffic around it to the network you want to protect, and if (3) that second router is also well-configured to prevent n adversary from taking control of it bypassing it, then (and only then) does the second router approach meaningfully make your network more protected from Internet-based infiltration attacks.
Now, from the facts you presented above, to my eye it lloks like you probably have met those three requirements. Good. You are more secure against Internet-side infiltration attacks that you would be if you just had either the netgear router or Linksys router alone. Now here's the bad news: the traditional infiltration hack (meaning taking control of or making use of some severe misconfiguration in some device in order to then create a pathway to get into a targeted internal network you aren't supposed to be in) is merely one kind of many kinds of attacks that you have to worry about. Indeed, precisely because most consumer routers today have fair-enough protection against that threat that other attack vectors have become more worrisome for the vast, vast majority of people.
Threat vectors like:
-Drive-by-download browser-based attacks to get malware on your PCs/tablets/phones
-Poisoned document files (PDF, Office file-format, and occasionally other document files) contaminated with malware & spread by email, messaging apps, etc. through phishing & spear-phishing campaigns.
-Other kinds of phishing campaigns that attempt to deceive you into typing your log-in info for an online service into a counterfeit website
-Physical loss or theft of mobile devices that have information you want to keep confidential stored of them.
-And many, many, many others.
So, to be honest, in terms of spending time and other resources that you could be using instead to help defend against other types of security risks (like those mentioned above), in most cases I would tell a client not to spend a whole lot of time implementing a two-router setup. (There are exceptions; I've implemented a dual-router approach for clients in other cases where I thought it added real security.) Instead, I would usually advise a typical user to, in rough order of priority, attend to these things:
-If you have solid suspicion that you might have malware on your devices, or that there still might be some malware remaining after a known previous infection, use a good malware scanner to look. More info on what to use, how, and how to deal with anything you find is available...well, in numerous pages right here, I'm sure. But also start preparing yourself for the possibility that you might eventually find that wiping and reinstalling your OS or OSes of choice is the only thing that will leave you feeling safe.
-Make sure the Operating Systems and all your firmware on all your devices are fully up-to-date with security updates (ie. fully patched), and any & all auto-update features available for downloading & installing those updates without users having to bother with doing anything are on and working.
-Make sure your programs are likewise fully patched and that any auto-updaters they come with are on and working. Especially browsers, browser add-ins/plug-ins, and document viewing & editing programs.
-On browsers: Unless you have a strong preference otherwise, use Google Chrome and/or Microsoft Edge for general day-to-day browsing. See if you can get by with turning the built-in Adobe Flash off for most uses and by using the PDF readers baked into the browsers (rather than Adobe Reader) most of the time. Also, security bonus: neither browser will now work with security-problem-plagued Java plug-ins.
-If you didn't have one already, I'd say buy a cost-effective SPI (Stateful Packet Inspection) router that doesn't have any currently known and unpatched horrible security vulnerabilities in its firmware. (Google or Bing is your friend.) Change the default user-name (if you can) and set a strong password. Check for said firmware updates. Make 100% sure any "remote administration" function is definitely set to off. Kill UnP to be safe. And that's... well, really that'll take care of blocking the kind of infiltration threats that I might expect a home/home office router to face. If you want to go more hardcore re. security capabilities you can upgrade to a business-class router or change out the cheap router maker's firmware for something like DD-WRT. (Oh, that reminds me, you might want to check DD-WRT compatibility before you buy. Just, you know, in case.)
-For every account or service that you care in any way about protecting, use a unique and not-obviously idiotic password. Use some sort of password-management program or system to keep track of those passwords.
-Oh, wifi setup, right. WPA2, of course. Long passkey, longer than almost any password you could have, and have plenty of pseudo-randomly chosen characters (or words, actually, as long as they're sufficiently random) for purpose of adding complexity. Any blasted WPS "feature" off. Guest account off, until/if you ever have guests to use it.
-For PCs create both a user-level account and an administrator account. Run as a user for day-to-day well, usage, and as an administrator only when you need to do administrator things without security prompts aggravating you.
-Turn on two-factor authentication everywhere you can.
-Be skeptical and suspicious of all links, documents, and other files contained in messages of all types (email, messaging apps, Facebook wall posts, Facebook messages, tweets, every means of electronically communicating information that you can think of). Even if you know the sender.
-Install only programs and apps you've looked at a bit, and only from trusted sources (ie., the Amazon, Apple, Google, Microsoft app stores). If we're talking about legacy Windows programs, presume any one of them that you haven't done some good homework investigating is either outright malicious or harmful to your privacy. [Don't get me wrong, I'm a Windows guy. But if you're downloading Win32 applications you found on the Internet you gotta be sure of what you're doing.]
In other words, pay attention to the basics. And, well...back up important stuff off-line just in case. Unless you've got super important stuff to protect, focus on the basics and back stuff up. And then go have fun setting up multiple-level router networks if you have the time and inclination later.
And if you do have super-important stuff to protect?
Start by focusing on the basics and backing stuff up.
