Since you are coming at this from a privacy standpoint, I'd suggest a router that runs some type of open source firmware such as OpenWRT. GL.iNet makes some good routers with their own fork of OpenWRT which has a very easy to use and intuitive UI as opposed to flashing OpenWRT to a supported router (setup then is very complicated).

Many routers out there will spy on you, make it difficult or impossible to set up privacy features, and have limited software updates for security patches.

The GL.iNet Flint 2 is a modern, fast router and makes it easy to setup a VPN, supports AdGuard home, and setting custom DNS providers. I've had it since launch and its had numerous updates too.

A VPN and private DNS hide your internet traffic from your ISP who will undoubtedly sell your data. However, a VPN is a transfer of trust so you want to use one that is open source, audited, and has a good track record of not logging any data. IVPN, Mullvad, and Proton are good VPNs. Quad9 and NextDNS are great private DNS providers. AdGuard and PiHole will block ads through various means.

Watch videos from Naomi Brockwell to learn more about all this stuff.

The brand/type of wifi router is more of a technical requirements discussion than privacy discussion.

For instance, I live in a two story townhome rental with the modem in the basement - so I picked up an Orbi mesh system to bounce wifi up to the second floor. I also have a fairly complex network with IoT VLAN, DMZ (for remote VPN) and other network segments - again the orbi doing different VLANs per SSID was a deciding factor.

I've also only used the Orbi as an access point, relying on a dedicated firewall/router for that stuff.

If you're looking at a flat network (e.g. everything on one segment - the typical home user setup), pretty much any WiFi router from Best Buy or equivalent will do the job. Check your current devices to see if you can take advantage of WiFi 7 technology - otherwise save a few bucks and go WiFi 6.

For security purposes, change the default SSID (the wireless name) to something unique - and change the password to something from correcthorsebatterystaple.net. You don't need the default jumble of letters and numbers to be secure.

Lastly, getting to your privacy concerns, look at the DHCP settings - that's what hands out IP addresses to your devices so they can reach the internet. Change the DNS servers to something other than your ISP. This looks like a good starting point.

The big things are to make sure you don't expose your router management to the Internet (the default shouldn't do that) and to make sure you periodically check for firmware updates.

If you want to up your game, you could look at spinning up a self-hosted DNS server like Pi-Hole - but that can be a bit more advanced to get setup and troubleshoot if something goes wrong.

Any router from a mainstream brand is likely fine, just don't enable any of their "cloud" BS and don't use their smartphone app. I've had good luck with Asus, they have an app but you don't have to use it at all.

For security, try to enable WPA3 on your Wi-Fi networks, otherwise WPA2 is probably fine unless you're being targeted by a government-sponsored hacking operation. Choose a long password for your network.

Once you get it up and running, then worry about DNS and PiHole and VPNs and all that. Don't get in over your head.

Well, I can't help you much with what router to get, but one thing I do is use ControlD.com free DNS. They have several levels of blocking you can do for free. You can do no blocking at all, you can block known malware, you can block known malware, and advertising, or you can block known malware, advertising, and big social media. Since this is on the router DNS setting, it will apply to every device as long as it is on your network. And then you can also set it up on your Android or iPhone so that when you are on mobile data, it also keeps the same level of blocking.

https://www.privacyguides.org/en/basics/hardware/?h=networking#secure-your-network

Really you need to first define your threat model, the EFF has a good guide on that.

Maximum paranoia would be Wi-Fi only connects to a restricted VLAN that can only talk to a VPN server. You must use a VPN to access your network over wireless. That's probably too much work for most people. But it would be the most compartmentalized, not trusting Wi-Fi encryption, which really isn't that strong

Super basic data hygiene means you only use WPA2 and above security for your Wi-Fi network.

Depending on your actual threat model, what you choose to do will probably be between those two points.

That is a complex problem. When you say router I assume you mean the all in one units? The common off the shelf devices are a router, switch, firewall, dhcp server and WiFi access point. Depending on the hardware they are normally pretty solid for one or a few people. The key thing you should be concerned about is the software on the device. There are plenty of open firmwares for network devices but they normally expect you to have a decent understanding of networking. Software like OpenWRT does have some decent defaults but you need to know things like how to keep it updated and how to create a secure WiFi network in the GUI.

https://www.geeksforgeeks.org/introduction-of-a-router/

https://openwrt.org/

Turn off broadcast of the SSID (meaning that your network isn't seen when someone looks at available networks).

PiHole is probably more advanced than you're ready to explore given your present level of knowledge, but I'd encourage you to dive in if you consider the concept interesting. You might develop a new hobby. If you have a tech-interested friend, you might ask them to set one up on your behalf.

Oh, one other thing you may consider doing. Put your network on five gigahertz only and disable 2.4 gigahertz entirely because 2.4 gigahertz goes farther so somebody could try to hack your network from a physical longer distance away. Whereas on five gigahertz they would have to be physically closer to do so.

Do a Site Survey and make a Wi-Fi heat map of your current setup so you can figure out if you need any APs in specific areas.

To me, this is the most important and most overlooked thing you can do to prepare a wireless network.

I've personally had good luck with NetSpot but pretty sure you have to pay for the enterprise version to do a heatmap/site survey.

Brand doesn’t matter. They’re all equally bad.

There’s two passwords to change: your routers administrator password and your WiFi password.

There’s mainly one setting to disable, but it’s often broken up into many across several parts of the device’s configuration page: wan administration or access to anything under any circumstances.

The smart starting point with dns is: dns over https. It’s probably all you need so don’t worry about pihole or other stuff. You mentioned mullvad. Use theirs.

These recommendations will provide a good baseline for security that doesn’t break the places you want to go on the internet. You could do more on the client side like use a vpn from your computer or configure your browser to use encrypted client hello and never store cookies or cache.