OP, I don’t know much about the mesh systems but my understanding is that they broadcast the same network but from a series of devices that you place strategically around your home to give better coverage. Plug in extenders broadcast their own WiFi signal and even if you give it the same name and password as the main routers WiFi it will still be a different WiFi network.
Lots of people on here seem to love mesh systems so they might be great but not tried one myself but I have naim audio kit and Naim don’t recommend mesh for their stuff because they can “prevent devices on your network from talking to each other”
I saw a glowing review of the tp link archer C2300 router recently. £110 on Amazon. But there are loads out there.
All of the above is what I learned through research and trial and error, I’m not an IT professional.
If you’re using a router supplied by your ISP it’s likely to be shit anyway so more or less any aftermarket router or mesh system will be better.