I've done a lot of work putting WiFi into old buildings of the type you've described. It needs planning so that the mesh you establish is going to be viable. You'll find some "science" via this sticky post: https://community.virginmedia.com/t5/Networking-and-WiFi/UNDERSTANDING-KEY-ASPECTS-OF-WiFi/td-p/3870...
In essence you should consider surveying your property with an App that detects WiFi sources and display a signal strength. You should then map this on a per room or part room basis and note a position that receives a decent WiFi signal so that the mesh can propagate onwards. Then place an access point there (powered) and bridged to your WiFi source (Hub or private router). Then to the next spot and so on until you've got the house covered.
Whether or not you end up with Pods is up to you. But the survey needs doing because one device relays to the next and so on.
The very best solution (obviously not trivial) is to run Ethernet cables to any point where you wish to have an access point. Then you don't have any mesh worries. I don't think that the VM pods can take their source from Ethernet (they're a poor option). and governed by that wretched CONNECT app that you should avoid like the plague.
Another option, and a very valid one, is to buy Powerline Adaptors; you connect the first by Ethernet to your router and the others are served Internet over the electric mains. on a 1Gig service you'll maybe get up to 200 meg on the first floor and perhaps "only" 40 meg on the third floor; something like that. I've used them for years.
There is no simple solution to your requirements, from what I can gather.
As Seph said, Ethernet cables are best and the only reliable way to get top speeds. It can be a lot of work to drill through walls and ceilings and pull up floorboards, but so what? If I had to get such a job done I'd call in my electrician. It would be all over by the end of the day.
