Which broadband routers will work for me?

[DuncanMT]

Introduction(Ignore if TL;DR)

Hi everyone, I recently had a terrible experience with my broadband provider and the stability of the connection.  A few dropouts and constant fluctuations in speed every second so in games I was constantly rubber-banding. Its finally all fixed but during the process I noticed that my computer that is connected with WiFi (it has to be, its to far for cables and all the sockets near the router are used up with home plugs for other devices) got a substantially lower rating in speed tests than the one that was connected through the wall plug.

 

The point is I have decided that I may want to upgrade my router and WiFi dongle on my computer, maybe to wireless AC?  The problem is my broadband provider is TalkTalk(in the UK) and I have their super-fast fiber service.  What I want to know is which routers support this and how do I find out from their specifications.  

 

The router I currently have is the TalkTalk Super Router HG635 and is connection to the main outlet in my home using a grey DSL cable currently.

I also have a BT Openreach box somewhere that I was told to remove by TalkTalk.  They said that it isn't necessary now that I have the super router.

 

I have been looking at these products for my upgrade.

http://www.amazon.com/RT-AC66U-Dual-Band-Wireless-AC1750-Gigabit-Router/dp/B008ABOJKS%3Fpsc%3D1%26SubscriptionId%3D02B7Y8VZ2ZRE5MXHPMR2%26tag%3Dbestcoverycom-20%26linkCode%3Dxm2%26camp%3D2025%26creative%3D165953%26creativeASIN%3DB008ABOJKS

http://www.amazon.co.uk/NETGEAR-A6210-100PES-AC1200-802-11AC-Adapter/dp/B00OT586RQ/ref=sr_1_1?ie=UTF8&qid=1446649112&sr=8-1&keywords=wireless+ac+dongle

 

Are these good choices?  If yes/no, why?  Is it even worth upgrading?  Should I already know all this as a student studying Computer Science? Well, I am sure you will tell me soon enough