What's the best wireless adapter to use with my Wifi router?

Solution
It really depends on if you actually need the "fastest" and what you do with your router. If you have only say a 50m internet connection and you do not have a file server in your house likely any fairly modern nic will work fine. You are being limited by the internet connection well before your wireless will have a significant impact on the speed.

Still if you actually want the fastest you can look at something like

https://www.asus.com/Networking/PCEAC68/

There are other companies that sell similar cards from say tplink or netgear that cost a little less but are similar. The key feature is the ability to extend the antennas away from the back of the computer. This will in many cases greatly increase your signal levels and...
It really depends on if you actually need the "fastest" and what you do with your router. If you have only say a 50m internet connection and you do not have a file server in your house likely any fairly modern nic will work fine. You are being limited by the internet connection well before your wireless will have a significant impact on the speed.

Still if you actually want the fastest you can look at something like

https://www.asus.com/Networking/PCEAC68/

There are other companies that sell similar cards from say tplink or netgear that cost a little less but are similar. The key feature is the ability to extend the antennas away from the back of the computer. This will in many cases greatly increase your signal levels and give you a more stable connection. You also want 3 antenna...or better 4 to match your router.

So far I have not seen any nic card that has 4 antenna even 3 is hard to find. You will not be able to ever get the maximum speed off your router until they start selling nic cards like that. Then again the actually real life speed increase going from 2 antenna to 4 antenna is not as great as the manufacture pretend it is.
 
Solution
I have a router sitting next to my desktop PC and because of the thick walls in my house its range is just a few metres. I found that the best solution is to pass another ethernet cable under the stairs to another router some 10 metres away that services the rest of the house. I still get blind spots and I have now fixed this by adding these booster like gadgets: http://www.amazon.co.uk/TP-LINK-PA411KIT-Powerline-Adapter-Starter/dp/B0084Y9N3O/ref=sr_1_2?s=computers&ie=UTF8&qid=1445995398&sr=1-2&keywords=plug+in+dlink However I am a little concerned about how secure the system is with these gadgets. I also use these gadgets when I stay in hotels. They need to be reconfigured each time but boosts weak hotel wifi.