|The previous post is a little hard to understand. What the responder is trying to say is, you get much better performance from a wired connection than you will from wireless.|
So, if you're a gamer, you will want your gaming computer(s) and consoles connected with a network cable where possible. I know a wired connection on some consoles is not an option but on all your computers it should be so plug them in to the network, don't use them wirelessly.
If your computer network interface(s) are 1000 Mbps capable, both Cat5e and Cat6 are capable of that bandwidth and use the same type of ends (RJ45). I would recommend you just buy premade cables of the lengths you require.
With regard to what's the best router to buy, I would suggest that since you require wireless you'll want a dual band/dual radio unit that is capable of both 2.4 GHz and 5.0 GHz. All the newer wireless equipment is running at 5.0 GHz. Dual radios means all your legacy (2.4) will also be able to connect. Be sure to buy a unit that runs both concurrently (together). Some are only capable of running either one, or the other. You don't want that.
You will also want to ensure all LAN ports on your router are 1000 Mbps capable as well.
Which brand name isn't really relative as one is pretty much the same as the other. I recommend you spend some time, shop around and compare units. Read reviews! If 9 or 10 out of 10 reviews say it's a great unit, chances are it is. If 9 or 10 out of 10 say it's a POS, then chances are, it is. You can't go far wrong sticking with the bigger brand names like Linksys (Cisco), D-Link, etc.
Last but not least. Downloads and video streaming eat a lot of bandwidth. Doing either while gaming will affect your gaming performance even if you're on a wired connection to your router so you'll want to limit that during your gaming.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.