You have to understand that wireless bandwidth is shared between devices. So something like AC1300Mb means that bandwidth on one radio (5GHz Radio 1) is shared between all devices connected to it. When you're hooked up via ethernet you have a full 1Gb going to each devices (if supported). Does that make sense? Wireless is also half duplex, which means when it says you're connected at 300Mb it really means 150Mb speeds (which would still be fast enough for your internet package).
If you game on your laptop it's beneficial to go with a cable to reduce pings because local wireless adds latency (ms) to your online gaming. So say when I'm on BF4 and have a ping of 4ms if I'm on wireless that could be 10ms realistically.
Now to the rest, consumer routers and wireless technology aren't the best because they have to handle absolutely everything. NAT, local routing, packet handling, wireless client priority, ect ect. To properly setup a good wireless environment you want an enterprise wireless AP because they are made to handle high traffic and it takes the load off your already bogged down router/modem. So what I would do is buy something like this
AP and hook it up centralized in your house via ethernet to your router/modem and disable the wireless on your router/modem to reduce crosstalk.
The reason I was asking who your ISP was is because if you have Comcast, Time Warner Cable, Charter, or Cox you can get a Surfboard 6141 to handle the modem part and then route that to a better network setup granted money isn't a problem. I could set you up with a serious but practical setup if you wanted.
Edit: I guess it would be best to add this too. Wireless transmission rates also greatly vary depending on signal strength. If you have low signal your latency will be higher and bandwidth a lot lower.