You are partly correct.
The speed of the LAN side, that is the speed among all pcs on the LAN are limited to the speed of the router's LAN side switch and any other network switch. This is not an internet connection issue or matter.
Let's say you have 3 pcs and one large network attached storage on your LAN. Let's say that you have a network switch rated at 1 Gbps (1,000 Mbps) and the network storage is rated at 1 Gbps. Let's say that your pcs have older 100 Mbps network interface ports. Under this case, all 3 pcs could be uploading or downloading files to the network attached storage at 100 Mbps since the network switch and the network attached storage can run at 1 Gbps. Note that the network switch and the network attached storage are not used at their full speed (100 Mbps per pc x 3 pcs = 300 Mbps used when switch and storage can run at 1000 Mbps)
If you replace one pc with one that has a 1 Gbps network interface, and keep the other 2 which run a 100 Mbps, things change a bit. Now if all 3 run simultaneously; the two slower pcs will transfer at 100 Mbps and the 1000 Mbps will consume the rest of the capacity or about 700 Mbps.
Note all of the above is on the LAN side only; it assumes no internet traffic; in fact the above considers no Internet traffic.
Remember that in many non-home networks the LAN transfers a whole lot more data within the LAN than it transfers across the Internet.
Now to your question and issue:
1. You always want the LAN speed faster than the Internet speed; there are many cases where there is traffic within the LAN that needs to be addressed.
2. You do not want the pc to router speed to be a bottleneck or speed limiter when compared to Internet speed.
3. If your ISP max speed is 54 Mbps and you have one pc accessing internet, then the max speed you will see is 54 Mbps and the LAN 300 Mbps max speed would not be reached by internet traffic. However, you could consume 54 Mbps with internet and simultaneously share a file on the LAN at 300 - 54 Mbps = 246 Mbps in principal.
4. A wireless G at max 54 Mbps would not be able to deliver as illustrated in # 3 above because it is maxed at 54 Mbps, the ISP max speed.
Keep in mind that the LAN speed should always be faster than the Internet speed.
I hope this has helped.