My approach when faced with a similar issue was to go with Powerline+WiFi combined.
At each fixed device around the home I added a Homeplug. In most of these I then simply added a Wireless Access Point (similar to the one you posted above) and a switch if necessary. I had a lot of access points I'd acquired at uni when my friends all had WiFi in their rooms and then didn't need the kit after uni: if you're buying new equipment, get Homeplugs with several ethernet sockets and WiFi capability to save a bit of cash.
Obviously you don't need WiFi at every Homeplug if you have quite a few in close proximity, so you can leave it out from some of them. Similarly if you have a WiFi deadspot in your house you could add another Homeplug there. It's very flexible
This gives a cood combination of wired stability (I've found Homeplugs to be very reliable, although admittedly my electrical wiring is relatively recent) and WiFi coverage, with the added bonus that you aren't using WiFi as a backhaul (if you use pure WiFi range extenders, your traffic between access points has to be WiFi too, and you end up with less total throughput. By using the wires for backhaul you get a faster end result. The downside is that it's not that cheap, but it's also not overly expensive. For a 4 bedroom house you can probably do it for the cost of two non-WiFi homeplugs and two WiFi ones, for a total of about £150.
The things to look at
1) The ratio of Wired to Wireless items in your house (and how much they are used, relatively). If you can wire most things in, go for mostly Powerline with a couple of access points in the rooms you use most mobile stuff. If most of your kit is mobile, go for WiFi or for Homeplugs with lots of WiFi access points)
2) How much of the house you actually use WiFi in. If you only really use WiFi in the bedroom and Living Room, you can keep the costs down.
3) Wireless interference. In a large house you probably don't have too many neighbours nearby, but it's still worth checking how many WiFi networks are nearby and whether you have any clear channels available: if you're using WiFi extenders and access points, you need a lot of clear spectrum or you'll lose performance. I've really struggled with this in a block of flats.
But yeah, I'm VERY happy with my homeplug+WiFi combination. It gives the best of both worlds with the reliable connection of Wired/Powerline and the coverage of WiFi - with the caveat of my very congested WiFi due to living in an apartment (which the Homemplugs definitely help with) the only improvements I could make would be more 802.11ac WiFi kit and using Cat-6 cable to run ethernet around the house, but that would be a lot more work and cost.
