I just bought the Google Wifi System (3 unit mesh) and it's very cool. Strong signal throughout the house.
I've gone through several routers in the past few years and I've never had any issues with the Echo. Originally I did have an issue with too many WiFi devices on my ancient Linksys WRT54G router (probably about 10 years old). With this particular router, some WiFi devices would just drop off when it wasn't used for a period of time. For example, some of my Wemo switches would drop off the network because I didn't use that particular switch to turn on/off a light in that room for a couple of days. Then the Echo would have trouble finding it. Other routers I've used were much newer and never gave me any problems.
The only reason I went with the Google WiFi system was because of the superior mesh technology. This mesh technology is different than using WiFi extenders. With WiFi extenders, you have to lose a connection with your router before it will switch to the extender's connection. With Google mesh, it switches seamlessly and it always connects to the strongest access point. So if I was using my iPhone in the bedroom, it connects to the access point in the adjacent room. As I walk out towards the kitchen, it connects to the access point in the living room. It does this automatically and never loses a beat. Using the Google Wifi app, I can see which access point I'm connected to (as well as where all other devices are connected to). Another cool feature is that the 2.4GHz and the 5GHz bands are combined. They are both treated as the same network. Many people on this forum have found that when their Echo is connected to the 5GHz band on their router, the Echo can't see devices on the 2.4GHz band. This is completely eliminated. Both bands have the same SSID name and it doesn't matter which band you connect to. They are the same network.
My only complaint about the Google WiFi system is that there are no advanced settings that many other routers have. But the benefits outweigh the lack of advanced settings by far. So I'm happy that I got the Google WiFi system.